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100644 index 0000000..1dd1d5e --- /dev/null +++ b/help/en_US/scilab_en_US_help/_LaTeX_linprog.xml_1.png diff --git a/help/en_US/scilab_en_US_help/fgoalattain.html b/help/en_US/scilab_en_US_help/fgoalattain.html new file mode 100644 index 0000000..a9aa43d --- /dev/null +++ b/help/en_US/scilab_en_US_help/fgoalattain.html @@ -0,0 +1,195 @@ +<html><head> + <meta http-equiv="Content-Type" content="text/html; charset=utf-8"> + <title>fgoalattain</title> + <style type="text/css" media="all"> + @import url("scilab_code.css"); + @import url("xml_code.css"); + @import url("c_code.css"); + @import url("style.css"); + </style> + </head> + <body> + <div class="manualnavbar"> + <table width="100%"><tr> + <td width="30%"> + <span class="previous"><a href="section_19f4f1e5726c01d683e8b82be0a7e910.html"><< Symphony Toolbox</a></span> + + </td> + <td width="40%" class="center"> + <span class="top"><a href="section_19f4f1e5726c01d683e8b82be0a7e910.html">Symphony Toolbox</a></span> + + </td> + <td width="30%" class="next"> + <span class="next"><a href="fminbnd.html">fminbnd >></a></span> + + </td> + </tr></table> + <hr /> + </div> + + + + <span class="path"><a href="index.html">Symphony Toolbox</a> >> <a href="section_19f4f1e5726c01d683e8b82be0a7e910.html">Symphony Toolbox</a> > fgoalattain</span> + + <br /><br /> + <div class="refnamediv"><h1 class="refname">fgoalattain</h1> + <p class="refpurpose">Solves a multiobjective goal attainment problem</p></div> + + +<div class="refsynopsisdiv"><h3 class="title">Calling Sequence</h3> + <div class="synopsis"><pre><span class="default">x</span><span class="default"> = </span><span class="functionid">fgoalattain</span><span class="default">(</span><span class="default">fun</span><span class="default">,</span><span class="default">x0</span><span class="default">,</span><span class="default">goal</span><span class="default">,</span><span class="default">weight</span><span class="default">)</span> +<span class="default">x</span><span class="default"> = </span><span class="functionid">fgoalattain</span><span class="default">(</span><span class="default">fun</span><span class="default">,</span><span class="default">x0</span><span class="default">,</span><span class="default">goal</span><span class="default">,</span><span class="default">weight</span><span class="default">,</span><span class="default">A</span><span class="default">,</span><span class="default">b</span><span class="default">)</span> +<span class="default">x</span><span class="default"> = </span><span class="functionid">fgoalattain</span><span class="default">(</span><span class="default">fun</span><span class="default">,</span><span class="default">x0</span><span class="default">,</span><span class="default">goal</span><span class="default">,</span><span class="default">weight</span><span class="default">,</span><span class="default">A</span><span class="default">,</span><span class="default">b</span><span class="default">,</span><span class="default">Aeq</span><span class="default">,</span><span class="default">beq</span><span class="default">)</span> +<span class="default">x</span><span class="default"> = </span><span class="functionid">fgoalattain</span><span class="default">(</span><span class="default">fun</span><span class="default">,</span><span class="default">x0</span><span class="default">,</span><span class="default">goal</span><span class="default">,</span><span class="default">weight</span><span class="default">,</span><span class="default">A</span><span class="default">,</span><span class="default">b</span><span class="default">,</span><span class="default">Aeq</span><span class="default">,</span><span class="default">beq</span><span class="default">,</span><span class="default">lb</span><span class="default">,</span><span class="default">ub</span><span class="default">)</span> +<span class="default">x</span><span class="default"> = </span><span class="functionid">fgoalattain</span><span class="default">(</span><span class="default">fun</span><span class="default">,</span><span class="default">x0</span><span class="default">,</span><span class="default">goal</span><span class="default">,</span><span class="default">weight</span><span class="default">,</span><span class="default">A</span><span class="default">,</span><span class="default">b</span><span class="default">,</span><span class="default">Aeq</span><span class="default">,</span><span class="default">beq</span><span class="default">,</span><span class="default">lb</span><span class="default">,</span><span class="default">ub</span><span class="default">,</span><span class="default">nonlcon</span><span class="default">)</span> +<span class="default">x</span><span class="default"> = </span><span class="functionid">fgoalattain</span><span class="default">(</span><span class="default">fun</span><span class="default">,</span><span class="default">x0</span><span class="default">,</span><span class="default">goal</span><span class="default">,</span><span class="default">weight</span><span class="default">,</span><span class="default">A</span><span class="default">,</span><span class="default">b</span><span class="default">,</span><span class="default">Aeq</span><span class="default">,</span><span class="default">beq</span><span class="default">,</span><span class="default">lb</span><span class="default">,</span><span class="default">ub</span><span class="default">,</span><span class="default">nonlcon</span><span class="default">,</span><span class="default">options</span><span class="default">)</span> +<span class="default">[</span><span class="default">x</span><span class="default">,</span><span class="default">fval</span><span class="default">] = </span><span class="functionid">fgoalattain</span><span class="default">(...)</span> +<span class="default">[</span><span class="default">x</span><span class="default">,</span><span class="default">fval</span><span class="default">,</span><span class="default">attainfactor</span><span class="default">] = </span><span class="functionid">fgoalattain</span><span class="default">(...)</span> +<span class="default">[</span><span class="default">x</span><span class="default">,</span><span class="default">fval</span><span class="default">,</span><span class="default">attainfactor</span><span class="default">,</span><span class="default">exitflag</span><span class="default">] = </span><span class="functionid">fgoalattain</span><span class="default">(...)</span> +<span class="default">[</span><span class="default">x</span><span class="default">,</span><span class="default">fval</span><span class="default">,</span><span class="default">attainfactor</span><span class="default">,</span><span class="default">exitflag</span><span class="default">,</span><span class="default">output</span><span class="default">] = </span><span class="functionid">fgoalattain</span><span class="default">(...)</span> +<span class="default">[</span><span class="default">x</span><span class="default">,</span><span class="default">fval</span><span class="default">,</span><span class="default">attainfactor</span><span class="default">,</span><span class="default">exitflag</span><span class="default">,</span><span class="default">output</span><span class="default">,</span><span class="default">lambda</span><span class="default">] = </span><span class="functionid">fgoalattain</span><span class="default">(...)</span></pre></div></div> + +<div class="refsection"><h3 class="title">Parameters</h3> + <dl><dt><span class="term">fun:</span> + <dd><p class="para">a function that accepts a vector x and returns a vector F</p></dd></dt> + <dt><span class="term">x0:</span> + <dd><p class="para">a nx1 or 1xn matrix of double, where n is the number of variables.</p></dd></dt> + <dt><span class="term">A:</span> + <dd><p class="para">a nil x n matrix of double, where n is the number of variables and</p></dd></dt> + <dt><span class="term">b:</span> + <dd><p class="para">a nil x 1 matrix of double, where nil is the number of linear</p></dd></dt> + <dt><span class="term">Aeq:</span> + <dd><p class="para">a nel x n matrix of double, where n is the number of variables</p></dd></dt> + <dt><span class="term">beq:</span> + <dd><p class="para">a nel x 1 matrix of double, where nel is the number of linear</p></dd></dt> + <dt><span class="term">lb:</span> + <dd><p class="para">a nx1 or 1xn matrix of double, where n is the number of variables.</p></dd></dt> + <dt><span class="term">ub:</span> + <dd><p class="para">a nx1 or 1xn matrix of double, where n is the number of variables.</p></dd></dt> + <dt><span class="term">nonlcon:</span> + <dd><p class="para">a function, the nonlinear constraints</p></dd></dt> + <dt><span class="term">options :</span> + <dd><p class="para">a list, containing the option for user to specify. See below for details.</p></dd></dt> + <dt><span class="term">x:</span> + <dd><p class="para">a nx1 matrix of double, the computed solution of the optimization problem</p></dd></dt> + <dt><span class="term">fval:</span> + <dd><p class="para">a vector of double, the value of functions at x</p></dd></dt> + <dt><span class="term">attainfactor:</span> + <dd><p class="para">The amount of over- or underachievement of the goals,γ at the solution.</p></dd></dt> + <dt><span class="term">exitflag:</span> + <dd><p class="para">a 1x1 matrix of floating point integers, the exit status</p></dd></dt> + <dt><span class="term">output:</span> + <dd><p class="para">a struct, the details of the optimization process</p></dd></dt> + <dt><span class="term">lambda:</span> + <dd><p class="para">a struct, the Lagrange multipliers at optimum</p></dd></dt></dl></div> + +<div class="refsection"><h3 class="title">Description</h3> + <p class="para">fgoalattain solves the goal attainment problem, which is one formulation for minimizing a multiobjective optimization problem. +Finds the minimum of a problem specified by: +Minimise Y such that</p> + <p class="para"><span><img src='./_LaTeX_fgoalattain.xml_1.png' style='position:relative;top:64px;width:276px;height:136px'/></span></p> + <p class="para">The solver makes use of fmincon to find the minimum.</p> + <p class="para">The fgoalattain finds out the maximum value of Y for the objectives evaluated at the starting point and +adds that as another variable to the vector x +This is passed to the fmincon function to get the optimised value of Y +Hence, the algorithm used mainly is "ipopt" to obtain the optimum solution +The relations between f(x), Y, weights and goals are added as additional non-linear inequality constraints</p> + <p class="para">The options allows the user to set various parameters of the Optimization problem. +It should be defined as type "list" and contains the following fields. +<ul class="itemizedlist"><li>Syntax : options= list("MaxIter", [---], "CpuTime", [---], "GradObj", ---, "GradCon", ---);</li> +<li>MaxIter : a Scalar, containing the Maximum Number of Iteration that the solver should take.</li> +<li>CpuTime : a Scalar, containing the Maximum amount of CPU Time that the solver should take.</li> +<li>GradObj : a function, representing the gradient function of the Objective in Vector Form.</li> +<li>GradCon : a function, representing the gradient of the Non-Linear Constraints (both Equality and Inequality) of the problem. It is declared in such a way that gradient of non-linear inequality constraints are defined first as a separate Matrix (cg of size m2 X n or as an empty), followed by gradient of non-linear equality constraints as a separate Matrix (ceqg of size m2 X n or as an empty) where m2 & m3 are number of non-linear inequality and equality constraints respectively.</li> +<li>Default Values : options = list("MaxIter", [3000], "CpuTime", [600]);</li></ul></p> + <p class="para">By default, the gradient options for fminimax are turned off and and fmincon does the gradient opproximation of minmaxObjfun. In case the GradObj option is off and GradConstr option is on, fminimax approximates minmaxObjfun gradient using numderivative toolbox.</p> + <p class="para">If we can provide exact gradients, we should do so since it improves the convergence speed of the optimization algorithm.</p> + <p class="para">Furthermore, we must enable the "GradObj" option with the statement : +<div class="programlisting"><table border="0" width="100%"><tr><td width="98%"><pre class="scilabcode"><span class="scilabid">minimaxOptions</span> <span class="scilaboperator">=</span> <a class="scilabcommand" href="scilab://list">list</a><span class="scilabopenclose">(</span><span class="scilabstring">"</span><span class="scilabstring">GradObj</span><span class="scilabstring">"</span><span class="scilabdefault">,</span><span class="scilabid">fGrad</span><span class="scilabopenclose">)</span><span class="scilabdefault">;</span></pre></td><td valign="top"><a href="scilab://scilab.execexample/"><img src="ScilabExecute.png" border="0"/></a></td><td valign="top"><a href="scilab://scilab.editexample/"><img src="ScilabEdit.png" border="0"/></a></td><td></td></tr></table></div> +This will let fminimax know that the exact gradient of the objective function is known, so that it can change the calling sequence to the objective function. Note that, fGrad should be mentioned in the form of N x n where n is the number of variables, N is the number of functions in objective function.</p> + <p class="para">The constraint function must have header : +<div class="programlisting"><table border="0" width="100%"><tr><td width="98%"><pre class="scilabcode"><span class="scilabopenclose">[</span><span class="scilabid">c</span><span class="scilabdefault">,</span> <span class="scilabid">ceq</span><span class="scilabopenclose">]</span> <span class="scilaboperator">=</span> <span class="scilabid">confun</span><span class="scilabopenclose">(</span><span class="scilabid">x</span><span class="scilabopenclose">)</span></pre></td><td valign="top"><a href="scilab://scilab.execexample/"><img src="ScilabExecute.png" border="0"/></a></td><td valign="top"><a href="scilab://scilab.editexample/"><img src="ScilabEdit.png" border="0"/></a></td><td></td></tr></table></div> +where x is a n x 1 matrix of dominmaxUbles, c is a 1 x nni matrix of doubles and ceq is a 1 x nne matrix of doubles (nni : number of nonlinear inequality constraints, nne : number of nonlinear equality constraints). +On input, the variable x contains the current point and, on output, the variable c must contain the nonlinear inequality constraints and ceq must contain the nonlinear equality constraints.</p> + <p class="para">By default, the gradient options for fminimax are turned off and and fmincon does the gradient opproximation of confun. In case the GradObj option is on and GradCons option is off, fminimax approximates confun gradient using numderivative toolbox.</p> + <p class="para">If we can provide exact gradients, we should do so since it improves the convergence speed of the optimization algorithm.</p> + <p class="para">Furthermore, we must enable the "GradCon" option with the statement : +<div class="programlisting"><table border="0" width="100%"><tr><td width="98%"><pre class="scilabcode"><span class="scilabid">minimaxOptions</span> <span class="scilaboperator">=</span> <a class="scilabcommand" href="scilab://list">list</a><span class="scilabopenclose">(</span><span class="scilabstring">"</span><span class="scilabstring">GradCon</span><span class="scilabstring">"</span><span class="scilabdefault">,</span><span class="scilabid">confunGrad</span><span class="scilabopenclose">)</span><span class="scilabdefault">;</span></pre></td><td valign="top"><a href="scilab://scilab.execexample/"><img src="ScilabExecute.png" border="0"/></a></td><td valign="top"><a href="scilab://scilab.editexample/"><img src="ScilabEdit.png" border="0"/></a></td><td></td></tr></table></div> +This will let fminimax know that the exact gradient of the objective function is known, so that it can change the calling sequence to the objective function.</p> + <p class="para">The constraint derivative function must have header : +<div class="programlisting"><table border="0" width="100%"><tr><td width="98%"><pre class="scilabcode"><span class="scilabopenclose">[</span><span class="scilabid">dc</span><span class="scilabdefault">,</span><span class="scilabid">dceq</span><span class="scilabopenclose">]</span> <span class="scilaboperator">=</span> <span class="scilabid">confungrad</span><span class="scilabopenclose">(</span><span class="scilabid">x</span><span class="scilabopenclose">)</span></pre></td><td valign="top"><a href="scilab://scilab.execexample/"><img src="ScilabExecute.png" border="0"/></a></td><td valign="top"><a href="scilab://scilab.editexample/"><img src="ScilabEdit.png" border="0"/></a></td><td></td></tr></table></div> +where dc is a nni x n matrix of doubles and dceq is a nne x n matrix of doubles.</p> + <p class="para">The exitflag allows to know the status of the optimization which is given back by Ipopt. +<ul class="itemizedlist"><li>exitflag=0 : Optimal Solution Found</li> +<li>exitflag=1 : Maximum Number of Iterations Exceeded. Output may not be optimal.</li> +<li>exitflag=2 : Maximum amount of CPU Time exceeded. Output may not be optimal.</li> +<li>exitflag=3 : Stop at Tiny Step.</li> +<li>exitflag=4 : Solved To Acceptable Level.</li> +<li>exitflag=5 : Converged to a point of local infeasibility.</li></ul></p> + <p class="para">For more details on exitflag see the ipopt documentation, go to http://www.coin-or.org/Ipopt/documentation/</p> + <p class="para">The output data structure contains detailed informations about the optimization process. +It has type "struct" and contains the following fields. +<ul class="itemizedlist"><li>output.Iterations: The number of iterations performed during the search</li> +<li>output.Cpu_Time: The total cpu-time spend during the search</li> +<li>output.Objective_Evaluation: The number of Objective Evaluations performed during the search</li> +<li>output.Dual_Infeasibility: The Dual Infeasiblity of the final soution</li></ul></p> + <p class="para">The lambda data structure contains the Lagrange multipliers at the end +of optimization. In the current version the values are returned only when the the solution is optimal. +It has type "struct" and contains the following fields. +<ul class="itemizedlist"><li>lambda.lower: The Lagrange multipliers for the lower bound constraints.</li> +<li>lambda.upper: The Lagrange multipliers for the upper bound constraints.</li> +<li>lambda.eqlin: The Lagrange multipliers for the linear equality constraints.</li> +<li>lambda.ineqlin: The Lagrange multipliers for the linear inequality constraints.</li> +<li>lambda.eqnonlin: The Lagrange multipliers for the non-linear equality constraints.</li> +<li>lambda.ineqnonlin: The Lagrange multipliers for the non-linear inequality constraints.</li></ul></p> + <p class="para"></p></div> + +<div class="refsection"><h3 class="title">Examples</h3> + <div class="programlisting"><table border="0" width="100%"><tr><td width="98%"><pre class="scilabcode"><span class="scilabfkeyword">function</span> <span class="scilabinputoutputargs">f1</span><span class="scilaboperator">=</span><span class="scilabfunctionid">gattainObjfun</span><span class="scilabopenclose">(</span><span class="scilabinputoutputargs">x</span><span class="scilabopenclose">)</span> +<span class="scilabinputoutputargs">f1</span><span class="scilabopenclose">(</span><span class="scilabnumber">1</span><span class="scilabopenclose">)</span><span class="scilaboperator">=</span><span class="scilabnumber">2</span><span class="scilaboperator">*</span><span class="scilabinputoutputargs">x</span><span class="scilabopenclose">(</span><span class="scilabnumber">1</span><span class="scilabopenclose">)</span><span class="scilaboperator">*</span><span class="scilabinputoutputargs">x</span><span class="scilabopenclose">(</span><span class="scilabnumber">1</span><span class="scilabopenclose">)</span><span class="scilaboperator">+</span><span class="scilabinputoutputargs">x</span><span class="scilabopenclose">(</span><span class="scilabnumber">2</span><span class="scilabopenclose">)</span><span class="scilaboperator">*</span><span class="scilabinputoutputargs">x</span><span class="scilabopenclose">(</span><span class="scilabnumber">2</span><span class="scilabopenclose">)</span><span class="scilaboperator">-</span><span class="scilabnumber">48</span><span class="scilaboperator">*</span><span class="scilabinputoutputargs">x</span><span class="scilabopenclose">(</span><span class="scilabnumber">1</span><span class="scilabopenclose">)</span><span class="scilaboperator">-</span><span class="scilabnumber">40</span><span class="scilaboperator">*</span><span class="scilabinputoutputargs">x</span><span class="scilabopenclose">(</span><span class="scilabnumber">2</span><span class="scilabopenclose">)</span><span class="scilaboperator">+</span><span class="scilabnumber">304</span> +<span class="scilabinputoutputargs">f1</span><span class="scilabopenclose">(</span><span class="scilabnumber">2</span><span class="scilabopenclose">)</span><span class="scilaboperator">=</span><span class="scilaboperator">-</span><span class="scilabinputoutputargs">x</span><span class="scilabopenclose">(</span><span class="scilabnumber">1</span><span class="scilabopenclose">)</span><span class="scilaboperator">*</span><span class="scilabinputoutputargs">x</span><span class="scilabopenclose">(</span><span class="scilabnumber">1</span><span class="scilabopenclose">)</span><span class="scilaboperator">-</span><span class="scilabnumber">3</span><span class="scilaboperator">*</span><span class="scilabinputoutputargs">x</span><span class="scilabopenclose">(</span><span class="scilabnumber">2</span><span class="scilabopenclose">)</span><span class="scilaboperator">*</span><span class="scilabinputoutputargs">x</span><span class="scilabopenclose">(</span><span class="scilabnumber">2</span><span class="scilabopenclose">)</span> +<span class="scilabinputoutputargs">f1</span><span class="scilabopenclose">(</span><span class="scilabnumber">3</span><span class="scilabopenclose">)</span><span class="scilaboperator">=</span><span class="scilabinputoutputargs">x</span><span class="scilabopenclose">(</span><span class="scilabnumber">1</span><span class="scilabopenclose">)</span><span class="scilaboperator">+</span><span class="scilabnumber">3</span><span class="scilaboperator">*</span><span class="scilabinputoutputargs">x</span><span class="scilabopenclose">(</span><span class="scilabnumber">2</span><span class="scilabopenclose">)</span><span class="scilaboperator">-</span><span class="scilabnumber">18</span> +<span class="scilabinputoutputargs">f1</span><span class="scilabopenclose">(</span><span class="scilabnumber">4</span><span class="scilabopenclose">)</span><span class="scilaboperator">=</span><span class="scilaboperator">-</span><span class="scilabinputoutputargs">x</span><span class="scilabopenclose">(</span><span class="scilabnumber">1</span><span class="scilabopenclose">)</span><span class="scilaboperator">-</span><span class="scilabinputoutputargs">x</span><span class="scilabopenclose">(</span><span class="scilabnumber">2</span><span class="scilabopenclose">)</span> +<span class="scilabinputoutputargs">f1</span><span class="scilabopenclose">(</span><span class="scilabnumber">5</span><span class="scilabopenclose">)</span><span class="scilaboperator">=</span><span class="scilabinputoutputargs">x</span><span class="scilabopenclose">(</span><span class="scilabnumber">1</span><span class="scilabopenclose">)</span><span class="scilaboperator">+</span><span class="scilabinputoutputargs">x</span><span class="scilabopenclose">(</span><span class="scilabnumber">2</span><span class="scilabopenclose">)</span><span class="scilaboperator">-</span><span class="scilabnumber">8</span> +<span class="scilabfkeyword">endfunction</span> +<span class="scilabid">x0</span><span class="scilaboperator">=</span><span class="scilabopenclose">[</span><span class="scilaboperator">-</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilabnumber">1</span><span class="scilabopenclose">]</span><span class="scilabdefault">;</span> + +<span class="scilabid">goal</span><span class="scilaboperator">=</span><span class="scilabopenclose">[</span><span class="scilaboperator">-</span><span class="scilabnumber">5</span><span class="scilabdefault">,</span><span class="scilaboperator">-</span><span class="scilabnumber">3</span><span class="scilabdefault">,</span><span class="scilaboperator">-</span><span class="scilabnumber">2</span><span class="scilabdefault">,</span><span class="scilaboperator">-</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilaboperator">-</span><span class="scilabnumber">4</span><span class="scilabopenclose">]</span><span class="scilabdefault">;</span> +<span class="scilabid">weight</span><span class="scilaboperator">=</span><a class="scilabcommand" href="scilab://abs">abs</a><span class="scilabopenclose">(</span><span class="scilabid">goal</span><span class="scilabopenclose">)</span> +<span class="scilabid">gval</span> <span class="scilaboperator">=</span> +<span class="scilabopenclose">[</span><span class="scilaboperator">-</span> <span class="scilabnumber">0.0000011</span> +<span class="scilaboperator">-</span> <span class="scilabnumber">63.999998</span> +<span class="scilaboperator">-</span> <span class="scilabnumber">2.0000002</span> +<span class="scilaboperator">-</span> <span class="scilabnumber">8.</span> +<span class="scilabnumber">3.485D-08</span><span class="scilabopenclose">]</span> +<span class="scilabid">z</span> <span class="scilaboperator">=</span> +<span class="scilabopenclose">[</span><span class="scilabnumber">4.</span> <span class="scilabnumber">3.99</span><span class="scilabopenclose">]</span> + +<span class="scilabid">Run</span> <span class="scilabid">fgoalattain</span> +<span class="scilabopenclose">[</span><span class="scilabid">x</span><span class="scilabdefault">,</span><span class="scilabid">fval</span><span class="scilabdefault">,</span><span class="scilabid">attainfactor</span><span class="scilabdefault">,</span><span class="scilabid">exitflag</span><span class="scilabdefault">,</span><span class="scilabid">output</span><span class="scilabdefault">,</span><span class="scilabid">lambda</span><span class="scilabopenclose">]</span><span class="scilaboperator">=</span><span class="scilabid">fgoalattain</span><span class="scilabopenclose">(</span><span class="scilabfunctionid">gattainObjfun</span><span class="scilabdefault">,</span><span class="scilabid">x0</span><span class="scilabdefault">,</span><span class="scilabid">goal</span><span class="scilabdefault">,</span><span class="scilabid">weight</span><span class="scilabopenclose">)</span></pre></td><td valign="top"><a href="scilab://scilab.execexample/"><img src="ScilabExecute.png" border="0"/></a></td><td valign="top"><a href="scilab://scilab.editexample/"><img src="ScilabEdit.png" border="0"/></a></td><td></td></tr></table></div></div> + +<div class="refsection"><h3 class="title">Authors</h3> + <ul class="itemizedlist"><li class="member">Prajwala TM, Sheetal Shalini , 2015</li></ul></div> + <br /> + + <div class="manualnavbar"> + <table width="100%"> + <tr><td colspan="3" class="next"><a href="http://bugzilla.scilab.org/enter_bug.cgi?product=Scilab%20software&component=Documentation%20pages" class="ulink">Report an issue</a></td></tr> +<tr> + <td width="30%"> + <span class="previous"><a href="section_19f4f1e5726c01d683e8b82be0a7e910.html"><< Symphony Toolbox</a></span> + + </td> + <td width="40%" class="center"> + <span class="top"><a href="section_19f4f1e5726c01d683e8b82be0a7e910.html">Symphony Toolbox</a></span> + + </td> + <td width="30%" class="next"> + <span class="next"><a href="fminbnd.html">fminbnd >></a></span> + + </td> + </tr></table> + <hr /> + </div> + </body> +</html> diff --git a/help/en_US/scilab_en_US_help/fminbnd.html b/help/en_US/scilab_en_US_help/fminbnd.html new file mode 100644 index 0000000..9b64d03 --- /dev/null +++ b/help/en_US/scilab_en_US_help/fminbnd.html @@ -0,0 +1,174 @@ +<html><head> + <meta http-equiv="Content-Type" content="text/html; charset=utf-8"> + <title>fminbnd</title> + <style type="text/css" media="all"> + @import url("scilab_code.css"); + @import url("xml_code.css"); + @import url("c_code.css"); + @import url("style.css"); + </style> + </head> + <body> + <div class="manualnavbar"> + <table width="100%"><tr> + <td width="30%"> + <span class="previous"><a href="fgoalattain.html"><< fgoalattain</a></span> + + </td> + <td width="40%" class="center"> + <span class="top"><a href="section_19f4f1e5726c01d683e8b82be0a7e910.html">Symphony Toolbox</a></span> + + </td> + <td width="30%" class="next"> + <span class="next"><a href="fmincon.html">fmincon >></a></span> + + </td> + </tr></table> + <hr /> + </div> + + + + <span class="path"><a href="index.html">Symphony Toolbox</a> >> <a href="section_19f4f1e5726c01d683e8b82be0a7e910.html">Symphony Toolbox</a> > fminbnd</span> + + <br /><br /> + <div class="refnamediv"><h1 class="refname">fminbnd</h1> + <p class="refpurpose">Solves a multi-variable optimization problem on a bounded interval</p></div> + + +<div class="refsynopsisdiv"><h3 class="title">Calling Sequence</h3> + <div class="synopsis"><pre><span class="default">xopt</span><span class="default"> = </span><span class="functionid">fminbnd</span><span class="default">(</span><span class="default">f</span><span class="default">,</span><span class="default">x1</span><span class="default">,</span><span class="default">x2</span><span class="default">)</span> +<span class="default">xopt</span><span class="default"> = </span><span class="functionid">fminbnd</span><span class="default">(</span><span class="default">f</span><span class="default">,</span><span class="default">x1</span><span class="default">,</span><span class="default">x2</span><span class="default">,</span><span class="default">options</span><span class="default">)</span> +<span class="default">[</span><span class="default">xopt</span><span class="default">,</span><span class="default">fopt</span><span class="default">] = </span><span class="functionid">fminbnd</span><span class="default">(.....)</span> +<span class="default">[</span><span class="default">xopt</span><span class="default">,</span><span class="default">fopt</span><span class="default">,</span><span class="default">exitflag</span><span class="default">]= </span><span class="functionid">fminbnd</span><span class="default">(.....)</span> +<span class="default">[</span><span class="default">xopt</span><span class="default">,</span><span class="default">fopt</span><span class="default">,</span><span class="default">exitflag</span><span class="default">,</span><span class="default">output</span><span class="default">]=</span><span class="functionid">fminbnd</span><span class="default">(.....)</span> +<span class="default">[</span><span class="default">xopt</span><span class="default">,</span><span class="default">fopt</span><span class="default">,</span><span class="default">exitflag</span><span class="default">,</span><span class="default">output</span><span class="default">,</span><span class="default">lambda</span><span class="default">]=</span><span class="functionid">fminbnd</span><span class="default">(.....)</span></pre></div></div> + +<div class="refsection"><h3 class="title">Parameters</h3> + <dl><dt><span class="term">f :</span> + <dd><p class="para">a function, representing the objective function of the problem</p></dd></dt> + <dt><span class="term">x1 :</span> + <dd><p class="para">a vector, containing the lower bound of the variables of size (1 X n) or (n X 1) where 'n' is the number of Variables, where n is number of Variables</p></dd></dt> + <dt><span class="term">x2 :</span> + <dd><p class="para">a vector, containing the upper bound of the variables of size (1 X n) or (n X 1) or (0 X 0) where 'n' is the number of Variables. If x2 is empty it means upper bound is +infinity</p></dd></dt> + <dt><span class="term">options :</span> + <dd><p class="para">a list, containing the option for user to specify. See below for details.</p></dd></dt> + <dt><span class="term">xopt :</span> + <dd><p class="para">a vector of doubles, containing the the computed solution of the optimization problem.</p></dd></dt> + <dt><span class="term">fopt :</span> + <dd><p class="para">a scalar of double, containing the the function value at x.</p></dd></dt> + <dt><span class="term">exitflag :</span> + <dd><p class="para">a scalar of integer, containing the flag which denotes the reason for termination of algorithm. See below for details.</p></dd></dt> + <dt><span class="term">output :</span> + <dd><p class="para">a structure, containing the information about the optimization. See below for details.</p></dd></dt> + <dt><span class="term">lambda :</span> + <dd><p class="para">a structure, containing the Lagrange multipliers of lower bound and upper bound at the optimized point. See below for details.</p></dd></dt></dl></div> + +<div class="refsection"><h3 class="title">Description</h3> + <p class="para">Search the minimum of a multi-variable function on bounded interval specified by : +Find the minimum of f(x) such that</p> + <p class="para"><span><img src='./_LaTeX_fminbnd.xml_1.png' style='position:relative;top:20px;width:219px;height:48px'/></span></p> + <p class="para">The routine calls Ipopt for solving the Bounded Optimization problem, Ipopt is a library written in C++.</p> + <p class="para">The options allows the user to set various parameters of the Optimization problem. +It should be defined as type "list" and contains the following fields. +<ul class="itemizedlist"><li>Syntax : options= list("MaxIter", [---], "CpuTime", [---], TolX, [----]);</li> +<li>MaxIter : a Scalar, containing the Maximum Number of Iteration that the solver should take.</li> +<li>CpuTime : a Scalar, containing the Maximum amount of CPU Time that the solver should take.</li> +<li>TolX : a Scalar, containing the Tolerance value that the solver should take.</li> +<li>Default Values : options = list("MaxIter", [3000], "CpuTime", [600], TolX, [1e-4]);</li></ul></p> + <p class="para">The exitflag allows to know the status of the optimization which is given back by Ipopt. +<ul class="itemizedlist"><li>exitflag=0 : Optimal Solution Found</li> +<li>exitflag=1 : Maximum Number of Iterations Exceeded. Output may not be optimal.</li> +<li>exitflag=2 : Maximum CPU Time exceeded. Output may not be optimal.</li> +<li>exitflag=3 : Stop at Tiny Step.</li> +<li>exitflag=4 : Solved To Acceptable Level.</li> +<li>exitflag=5 : Converged to a point of local infeasibility.</li></ul></p> + <p class="para">For more details on exitflag see the ipopt documentation, go to http://www.coin-or.org/Ipopt/documentation/</p> + <p class="para">The output data structure contains detailed informations about the optimization process. +It has type "struct" and contains the following fields. +<ul class="itemizedlist"><li>output.Iterations: The number of iterations performed during the search</li> +<li>output.Cpu_Time: The total cpu-time spend during the search</li> +<li>output.Objective_Evaluation: The number of Objective Evaluations performed during the search</li> +<li>output.Dual_Infeasibility: The Dual Infeasiblity of the final soution</li></ul></p> + <p class="para">The lambda data structure contains the Lagrange multipliers at the end +of optimization. In the current version the values are returned only when the the solution is optimal. +It has type "struct" and contains the following fields. +<ul class="itemizedlist"><li>lambda.lower: The Lagrange multipliers for the lower bound constraints.</li> +<li>lambda.upper: The Lagrange multipliers for the upper bound constraints.</li></ul></p> + <p class="para"></p></div> + +<div class="refsection"><h3 class="title">Examples</h3> + <div class="programlisting"><table border="0" width="100%"><tr><td width="98%"><pre class="scilabcode"><span class="scilabcomment">//Find x in R^6 such that it minimizes:</span> +<span class="scilabcomment">//f(x)= sin(x1) + sin(x2) + sin(x3) + sin(x4) + sin(x5) + sin(x6)</span> +<span class="scilabcomment">//-2 </span><span class="scilabcomment"><</span><span class="scilabcomment">= x1,x2,x3,x4,x5,x6 </span><span class="scilabcomment"><</span><span class="scilabcomment">= 2</span> +<span class="scilabcomment">//Objective function to be minimised</span> +<span class="scilabfkeyword">function</span> <span class="scilabinputoutputargs">y</span><span class="scilaboperator">=</span><span class="scilabfunctionid">f</span><span class="scilabopenclose">(</span><span class="scilabinputoutputargs">x</span><span class="scilabopenclose">)</span> +<span class="scilabinputoutputargs">y</span><span class="scilaboperator">=</span><span class="scilabnumber">0</span> +<span class="scilabskeyword">for</span> <span class="scilabid">i</span> <span class="scilaboperator">=</span><span class="scilabnumber">1</span><span class="scilabspecial">:</span><span class="scilabnumber">6</span> +<span class="scilabinputoutputargs">y</span><span class="scilaboperator">=</span><span class="scilabinputoutputargs">y</span><span class="scilaboperator">+</span><a class="scilabcommand" href="scilab://sin">sin</a><span class="scilabopenclose">(</span><span class="scilabinputoutputargs">x</span><span class="scilabopenclose">(</span><span class="scilabid">i</span><span class="scilabopenclose">)</span><span class="scilabopenclose">)</span><span class="scilabdefault">;</span> +<span class="scilabskeyword">end</span> +<span class="scilabfkeyword">endfunction</span> +<span class="scilabcomment">//Variable bounds</span> +<span class="scilabid">x1</span> <span class="scilaboperator">=</span> <span class="scilabopenclose">[</span><span class="scilaboperator">-</span><span class="scilabnumber">2</span><span class="scilabdefault">,</span> <span class="scilaboperator">-</span><span class="scilabnumber">2</span><span class="scilabdefault">,</span> <span class="scilaboperator">-</span><span class="scilabnumber">2</span><span class="scilabdefault">,</span> <span class="scilaboperator">-</span><span class="scilabnumber">2</span><span class="scilabdefault">,</span> <span class="scilaboperator">-</span><span class="scilabnumber">2</span><span class="scilabdefault">,</span> <span class="scilaboperator">-</span><span class="scilabnumber">2</span><span class="scilabopenclose">]</span><span class="scilabdefault">;</span> +<span class="scilabid">x2</span> <span class="scilaboperator">=</span> <span class="scilabopenclose">[</span><span class="scilabnumber">2</span><span class="scilabdefault">,</span> <span class="scilabnumber">2</span><span class="scilabdefault">,</span> <span class="scilabnumber">2</span><span class="scilabdefault">,</span> <span class="scilabnumber">2</span><span class="scilabdefault">,</span> <span class="scilabnumber">2</span><span class="scilabdefault">,</span> <span class="scilabnumber">2</span><span class="scilabopenclose">]</span><span class="scilabdefault">;</span> +<span class="scilabcomment">//Options</span> +<span class="scilabid">options</span><span class="scilaboperator">=</span><a class="scilabcommand" href="scilab://list">list</a><span class="scilabopenclose">(</span><span class="scilabstring">"</span><span class="scilabstring">MaxIter</span><span class="scilabstring">"</span><span class="scilabdefault">,</span><span class="scilabopenclose">[</span><span class="scilabnumber">1500</span><span class="scilabopenclose">]</span><span class="scilabdefault">,</span><span class="scilabstring">"</span><span class="scilabstring">CpuTime</span><span class="scilabstring">"</span><span class="scilabdefault">,</span> <span class="scilabopenclose">[</span><span class="scilabnumber">100</span><span class="scilabopenclose">]</span><span class="scilabdefault">,</span><span class="scilabstring">"</span><span class="scilabstring">TolX</span><span class="scilabstring">"</span><span class="scilabdefault">,</span><span class="scilabopenclose">[</span><span class="scilabnumber">1e-6</span><span class="scilabopenclose">]</span><span class="scilabopenclose">)</span> +<span class="scilabcomment">//Calling Ipopt</span> +<span class="scilabopenclose">[</span><span class="scilabid">x</span><span class="scilabdefault">,</span><span class="scilabid">fval</span><span class="scilabopenclose">]</span> <span class="scilaboperator">=</span><span class="scilabid">fminbnd</span><span class="scilabopenclose">(</span><span class="scilabfunctionid">f</span><span class="scilabdefault">,</span> <span class="scilabid">x1</span><span class="scilabdefault">,</span> <span class="scilabid">x2</span><span class="scilabdefault">,</span> <span class="scilabid">options</span><span class="scilabopenclose">)</span></pre></td><td valign="top"><a href="scilab://scilab.execexample/"><img src="ScilabExecute.png" border="0"/></a></td><td valign="top"><a href="scilab://scilab.editexample/"><img src="ScilabEdit.png" border="0"/></a></td><td></td></tr></table></div></div> + +<div class="refsection"><h3 class="title">Examples</h3> + <div class="programlisting"><table border="0" width="100%"><tr><td width="98%"><pre class="scilabcode"><span class="scilabcomment">//Find x in R such that it minimizes:</span> +<span class="scilabcomment">//f(x)= 1/x^2</span> +<span class="scilabcomment">//0 </span><span class="scilabcomment"><</span><span class="scilabcomment">= x </span><span class="scilabcomment"><</span><span class="scilabcomment">= 1000</span> +<span class="scilabcomment">//Objective function to be minimised</span> +<span class="scilabfkeyword">function</span> <span class="scilabinputoutputargs">y</span><span class="scilaboperator">=</span><span class="scilabfunctionid">f</span><span class="scilabopenclose">(</span><span class="scilabinputoutputargs">x</span><span class="scilabopenclose">)</span> +<span class="scilabinputoutputargs">y</span><span class="scilaboperator">=</span><span class="scilabnumber">1</span><span class="scilaboperator">/</span><span class="scilabinputoutputargs">x</span><span class="scilaboperator">^</span><span class="scilabnumber">2</span> +<span class="scilabfkeyword">endfunction</span> +<span class="scilabcomment">//Variable bounds</span> +<span class="scilabid">x1</span> <span class="scilaboperator">=</span> <span class="scilabopenclose">[</span><span class="scilabnumber">0</span><span class="scilabopenclose">]</span><span class="scilabdefault">;</span> +<span class="scilabid">x2</span> <span class="scilaboperator">=</span> <span class="scilabopenclose">[</span><span class="scilabnumber">1000</span><span class="scilabopenclose">]</span><span class="scilabdefault">;</span> +<span class="scilabcomment">//Calling Ipopt</span> +<span class="scilabopenclose">[</span><span class="scilabid">x</span><span class="scilabdefault">,</span><span class="scilabid">fval</span><span class="scilabdefault">,</span><span class="scilabid">exitflag</span><span class="scilabdefault">,</span><span class="scilabid">output</span><span class="scilabdefault">,</span><span class="scilabid">lambda</span><span class="scilabopenclose">]</span> <span class="scilaboperator">=</span><span class="scilabid">fminbnd</span><span class="scilabopenclose">(</span><span class="scilabfunctionid">f</span><span class="scilabdefault">,</span> <span class="scilabid">x1</span><span class="scilabdefault">,</span> <span class="scilabid">x2</span><span class="scilabopenclose">)</span></pre></td><td valign="top"><a href="scilab://scilab.execexample/"><img src="ScilabExecute.png" border="0"/></a></td><td valign="top"><a href="scilab://scilab.editexample/"><img src="ScilabEdit.png" border="0"/></a></td><td></td></tr></table></div></div> + +<div class="refsection"><h3 class="title">Examples</h3> + <div class="programlisting"><table border="0" width="100%"><tr><td width="98%"><pre class="scilabcode"><span class="scilabcomment">//The below problem is an unbounded problem:</span> +<span class="scilabcomment">//Find x in R^2 such that it minimizes:</span> +<span class="scilabcomment">//f(x)= -[(x1-1)^2 + (x2-1)^2]</span> +<span class="scilabcomment">//-inf </span><span class="scilabcomment"><</span><span class="scilabcomment">= x1,x2 </span><span class="scilabcomment"><</span><span class="scilabcomment">= inf</span> +<span class="scilabcomment">//Objective function to be minimised</span> +<span class="scilabfkeyword">function</span> <span class="scilabinputoutputargs">y</span><span class="scilaboperator">=</span><span class="scilabfunctionid">f</span><span class="scilabopenclose">(</span><span class="scilabinputoutputargs">x</span><span class="scilabopenclose">)</span> +<span class="scilabinputoutputargs">y</span><span class="scilaboperator">=</span><span class="scilaboperator">-</span><span class="scilabopenclose">(</span><span class="scilabopenclose">(</span><span class="scilabinputoutputargs">x</span><span class="scilabopenclose">(</span><span class="scilabnumber">1</span><span class="scilabopenclose">)</span><span class="scilaboperator">-</span><span class="scilabnumber">1</span><span class="scilabopenclose">)</span><span class="scilaboperator">^</span><span class="scilabnumber">2</span><span class="scilaboperator">+</span><span class="scilabopenclose">(</span><span class="scilabinputoutputargs">x</span><span class="scilabopenclose">(</span><span class="scilabnumber">2</span><span class="scilabopenclose">)</span><span class="scilaboperator">-</span><span class="scilabnumber">1</span><span class="scilabopenclose">)</span><span class="scilaboperator">^</span><span class="scilabnumber">2</span><span class="scilabopenclose">)</span><span class="scilabdefault">;</span> +<span class="scilabfkeyword">endfunction</span> +<span class="scilabcomment">//Variable bounds</span> +<span class="scilabid">x1</span> <span class="scilaboperator">=</span> <span class="scilabopenclose">[</span><span class="scilaboperator">-</span><span class="scilabconstants">%inf</span> <span class="scilabdefault">,</span> <span class="scilaboperator">-</span><span class="scilabconstants">%inf</span><span class="scilabopenclose">]</span><span class="scilabdefault">;</span> +<span class="scilabid">x2</span> <span class="scilaboperator">=</span> <span class="scilabopenclose">[</span><span class="scilabopenclose">]</span><span class="scilabdefault">;</span> +<span class="scilabcomment">//Options</span> +<span class="scilabid">options</span><span class="scilaboperator">=</span><a class="scilabcommand" href="scilab://list">list</a><span class="scilabopenclose">(</span><span class="scilabstring">"</span><span class="scilabstring">MaxIter</span><span class="scilabstring">"</span><span class="scilabdefault">,</span><span class="scilabopenclose">[</span><span class="scilabnumber">1500</span><span class="scilabopenclose">]</span><span class="scilabdefault">,</span><span class="scilabstring">"</span><span class="scilabstring">CpuTime</span><span class="scilabstring">"</span><span class="scilabdefault">,</span> <span class="scilabopenclose">[</span><span class="scilabnumber">100</span><span class="scilabopenclose">]</span><span class="scilabdefault">,</span><span class="scilabstring">"</span><span class="scilabstring">TolX</span><span class="scilabstring">"</span><span class="scilabdefault">,</span><span class="scilabopenclose">[</span><span class="scilabnumber">1e-6</span><span class="scilabopenclose">]</span><span class="scilabopenclose">)</span> +<span class="scilabcomment">//Calling Ipopt</span> +<span class="scilabopenclose">[</span><span class="scilabid">x</span><span class="scilabdefault">,</span><span class="scilabid">fval</span><span class="scilabdefault">,</span><span class="scilabid">exitflag</span><span class="scilabdefault">,</span><span class="scilabid">output</span><span class="scilabdefault">,</span><span class="scilabid">lambda</span><span class="scilabopenclose">]</span> <span class="scilaboperator">=</span><span class="scilabid">fminbnd</span><span class="scilabopenclose">(</span><span class="scilabfunctionid">f</span><span class="scilabdefault">,</span> <span class="scilabid">x1</span><span class="scilabdefault">,</span> <span class="scilabid">x2</span><span class="scilabdefault">,</span> <span class="scilabid">options</span><span class="scilabopenclose">)</span></pre></td><td valign="top"><a href="scilab://scilab.execexample/"><img src="ScilabExecute.png" border="0"/></a></td><td valign="top"><a href="scilab://scilab.editexample/"><img src="ScilabEdit.png" border="0"/></a></td><td></td></tr></table></div></div> + +<div class="refsection"><h3 class="title">Authors</h3> + <ul class="itemizedlist"><li class="member">R.Vidyadhar , Vignesh Kannan</li></ul></div> + <br /> + + <div class="manualnavbar"> + <table width="100%"> + <tr><td colspan="3" class="next"><a href="http://bugzilla.scilab.org/enter_bug.cgi?product=Scilab%20software&component=Documentation%20pages" class="ulink">Report an issue</a></td></tr> +<tr> + <td width="30%"> + <span class="previous"><a href="fgoalattain.html"><< fgoalattain</a></span> + + </td> + <td width="40%" class="center"> + <span class="top"><a href="section_19f4f1e5726c01d683e8b82be0a7e910.html">Symphony Toolbox</a></span> + + </td> + <td width="30%" class="next"> + <span class="next"><a href="fmincon.html">fmincon >></a></span> + + </td> + </tr></table> + <hr /> + </div> + </body> +</html> diff --git a/help/en_US/scilab_en_US_help/fmincon.html b/help/en_US/scilab_en_US_help/fmincon.html new file mode 100644 index 0000000..242c58b --- /dev/null +++ b/help/en_US/scilab_en_US_help/fmincon.html @@ -0,0 +1,302 @@ +<html><head> + <meta http-equiv="Content-Type" content="text/html; charset=utf-8"> + <title>fmincon</title> + <style type="text/css" media="all"> + @import url("scilab_code.css"); + @import url("xml_code.css"); + @import url("c_code.css"); + @import url("style.css"); + </style> + </head> + <body> + <div class="manualnavbar"> + <table width="100%"><tr> + <td width="30%"> + <span class="previous"><a href="fminbnd.html"><< fminbnd</a></span> + + </td> + <td width="40%" class="center"> + <span class="top"><a href="section_19f4f1e5726c01d683e8b82be0a7e910.html">Symphony Toolbox</a></span> + + </td> + <td width="30%" class="next"> + <span class="next"><a href="fminunc.html">fminunc >></a></span> + + </td> + </tr></table> + <hr /> + </div> + + + + <span class="path"><a href="index.html">Symphony Toolbox</a> >> <a href="section_19f4f1e5726c01d683e8b82be0a7e910.html">Symphony Toolbox</a> > fmincon</span> + + <br /><br /> + <div class="refnamediv"><h1 class="refname">fmincon</h1> + <p class="refpurpose">Solves a multi-variable constrainted optimization problem</p></div> + + +<div class="refsynopsisdiv"><h3 class="title">Calling Sequence</h3> + <div class="synopsis"><pre><span class="default">xopt</span><span class="default"> = </span><span class="functionid">fmincon</span><span class="default">(</span><span class="default">f</span><span class="default">,</span><span class="default">x0</span><span class="default">,</span><span class="default">A</span><span class="default">,</span><span class="default">b</span><span class="default">)</span> +<span class="default">xopt</span><span class="default"> = </span><span class="functionid">fmincon</span><span class="default">(</span><span class="default">f</span><span class="default">,</span><span class="default">x0</span><span class="default">,</span><span class="default">A</span><span class="default">,</span><span class="default">b</span><span class="default">,</span><span class="default">Aeq</span><span class="default">,</span><span class="default">beq</span><span class="default">)</span> +<span class="default">xopt</span><span class="default"> = </span><span class="functionid">fmincon</span><span class="default">(</span><span class="default">f</span><span class="default">,</span><span class="default">x0</span><span class="default">,</span><span class="default">A</span><span class="default">,</span><span class="default">b</span><span class="default">,</span><span class="default">Aeq</span><span class="default">,</span><span class="default">beq</span><span class="default">,</span><span class="default">lb</span><span class="default">,</span><span class="default">ub</span><span class="default">)</span> +<span class="default">xopt</span><span class="default"> = </span><span class="functionid">fmincon</span><span class="default">(</span><span class="default">f</span><span class="default">,</span><span class="default">x0</span><span class="default">,</span><span class="default">A</span><span class="default">,</span><span class="default">b</span><span class="default">,</span><span class="default">Aeq</span><span class="default">,</span><span class="default">beq</span><span class="default">,</span><span class="default">lb</span><span class="default">,</span><span class="default">ub</span><span class="default">,</span><span class="default">nlc</span><span class="default">)</span> +<span class="default">xopt</span><span class="default"> = </span><span class="functionid">fmincon</span><span class="default">(</span><span class="default">f</span><span class="default">,</span><span class="default">x0</span><span class="default">,</span><span class="default">A</span><span class="default">,</span><span class="default">b</span><span class="default">,</span><span class="default">Aeq</span><span class="default">,</span><span class="default">beq</span><span class="default">,</span><span class="default">lb</span><span class="default">,</span><span class="default">ub</span><span class="default">,</span><span class="default">nlc</span><span class="default">,</span><span class="default">options</span><span class="default">)</span> +<span class="default">[</span><span class="default">xopt</span><span class="default">,</span><span class="default">fopt</span><span class="default">] = </span><span class="functionid">fmincon</span><span class="default">(.....)</span> +<span class="default">[</span><span class="default">xopt</span><span class="default">,</span><span class="default">fopt</span><span class="default">,</span><span class="default">exitflag</span><span class="default">]= </span><span class="functionid">fmincon</span><span class="default">(.....)</span> +<span class="default">[</span><span class="default">xopt</span><span class="default">,</span><span class="default">fopt</span><span class="default">,</span><span class="default">exitflag</span><span class="default">,</span><span class="default">output</span><span class="default">]= </span><span class="functionid">fmincon</span><span class="default">(.....)</span> +<span class="default">[</span><span class="default">xopt</span><span class="default">,</span><span class="default">fopt</span><span class="default">,</span><span class="default">exitflag</span><span class="default">,</span><span class="default">output</span><span class="default">,</span><span class="default">lambda</span><span class="default">]=</span><span class="functionid">fmincon</span><span class="default">(.....)</span> +<span class="default">[</span><span class="default">xopt</span><span class="default">,</span><span class="default">fopt</span><span class="default">,</span><span class="default">exitflag</span><span class="default">,</span><span class="default">output</span><span class="default">,</span><span class="default">lambda</span><span class="default">,</span><span class="default">gradient</span><span class="default">]=</span><span class="functionid">fmincon</span><span class="default">(.....)</span> +<span class="default">[</span><span class="default">xopt</span><span class="default">,</span><span class="default">fopt</span><span class="default">,</span><span class="default">exitflag</span><span class="default">,</span><span class="default">output</span><span class="default">,</span><span class="default">lambda</span><span class="default">,</span><span class="default">gradient</span><span class="default">,</span><span class="default">hessian</span><span class="default">]=</span><span class="functionid">fmincon</span><span class="default">(.....)</span></pre></div></div> + +<div class="refsection"><h3 class="title">Parameters</h3> + <dl><dt><span class="term">f :</span> + <dd><p class="para">a function, representing the objective function of the problem</p></dd></dt> + <dt><span class="term">x0 :</span> + <dd><p class="para">a vector of doubles, containing the starting values of variables of size (1 X n) or (n X 1) where 'n' is the number of Variables</p></dd></dt> + <dt><span class="term">A :</span> + <dd><p class="para">a matrix of doubles, containing the coefficients of linear inequality constraints of size (m X n) where 'm' is the number of linear inequality constraints</p></dd></dt> + <dt><span class="term">b :</span> + <dd><p class="para">a vector of doubles, related to 'A' and containing the the Right hand side equation of the linear inequality constraints of size (m X 1)</p></dd></dt> + <dt><span class="term">Aeq :</span> + <dd><p class="para">a matrix of doubles, containing the coefficients of linear equality constraints of size (m1 X n) where 'm1' is the number of linear equality constraints</p></dd></dt> + <dt><span class="term">beq :</span> + <dd><p class="para">a vector of doubles, related to 'Aeq' and containing the the Right hand side equation of the linear equality constraints of size (m1 X 1)</p></dd></dt> + <dt><span class="term">lb :</span> + <dd><p class="para">a vector of doubles, containing the lower bounds of the variables of size (1 X n) or (n X 1) where 'n' is the number of Variables</p></dd></dt> + <dt><span class="term">ub :</span> + <dd><p class="para">a vector of doubles, containing the upper bounds of the variables of size (1 X n) or (n X 1) where 'n' is the number of Variables</p></dd></dt> + <dt><span class="term">nlc :</span> + <dd><p class="para">a function, representing the Non-linear Constraints functions(both Equality and Inequality) of the problem. It is declared in such a way that non-linear inequality constraints are defined first as a single row vector (c), followed by non-linear equality constraints as another single row vector (ceq). Refer Example for definition of Constraint function.</p></dd></dt> + <dt><span class="term">options :</span> + <dd><p class="para">a list, containing the option for user to specify. See below for details.</p></dd></dt> + <dt><span class="term">xopt :</span> + <dd><p class="para">a vector of doubles, cointating the computed solution of the optimization problem</p></dd></dt> + <dt><span class="term">fopt :</span> + <dd><p class="para">a scalar of double, containing the the function value at x</p></dd></dt> + <dt><span class="term">exitflag :</span> + <dd><p class="para">a scalar of integer, containing the flag which denotes the reason for termination of algorithm. See below for details.</p></dd></dt> + <dt><span class="term">output :</span> + <dd><p class="para">a structure, containing the information about the optimization. See below for details.</p></dd></dt> + <dt><span class="term">lambda :</span> + <dd><p class="para">a structure, containing the Lagrange multipliers of lower bound, upper bound and constraints at the optimized point. See below for details.</p></dd></dt> + <dt><span class="term">gradient :</span> + <dd><p class="para">a vector of doubles, containing the Objective's gradient of the solution.</p></dd></dt> + <dt><span class="term">hessian :</span> + <dd><p class="para">a matrix of doubles, containing the Lagrangian's hessian of the solution.</p></dd></dt></dl></div> + +<div class="refsection"><h3 class="title">Description</h3> + <p class="para">Search the minimum of a constrained optimization problem specified by : +Find the minimum of f(x) such that</p> + <p class="para"><span><img src='./_LaTeX_fmincon.xml_1.png' style='position:relative;top:63px;width:221px;height:134px'/></span></p> + <p class="para">The routine calls Ipopt for solving the Constrained Optimization problem, Ipopt is a library written in C++.</p> + <p class="para">The options allows the user to set various parameters of the Optimization problem. +It should be defined as type "list" and contains the following fields. +<ul class="itemizedlist"><li>Syntax : options= list("MaxIter", [---], "CpuTime", [---], "GradObj", ---, "Hessian", ---, "GradCon", ---);</li> +<li>MaxIter : a Scalar, containing the Maximum Number of Iteration that the solver should take.</li> +<li>CpuTime : a Scalar, containing the Maximum amount of CPU Time that the solver should take.</li> +<li>GradObj : a function, representing the gradient function of the Objective in Vector Form.</li> +<li>Hessian : a function, representing the hessian function of the Lagrange in Symmetric Matrix Form with Input parameters x, Objective factor and Lambda. Refer Example for definition of Lagrangian Hessian function.</li> +<li>GradCon : a function, representing the gradient of the Non-Linear Constraints (both Equality and Inequality) of the problem. It is declared in such a way that gradient of non-linear inequality constraints are defined first as a separate Matrix (cg of size m2 X n or as an empty), followed by gradient of non-linear equality constraints as a separate Matrix (ceqg of size m2 X n or as an empty) where m2 & m3 are number of non-linear inequality and equality constraints respectively.</li> +<li>Default Values : options = list("MaxIter", [3000], "CpuTime", [600]);</li></ul></p> + <p class="para">The exitflag allows to know the status of the optimization which is given back by Ipopt. +<ul class="itemizedlist"><li>exitflag=0 : Optimal Solution Found</li> +<li>exitflag=1 : Maximum Number of Iterations Exceeded. Output may not be optimal.</li> +<li>exitflag=2 : Maximum amount of CPU Time exceeded. Output may not be optimal.</li> +<li>exitflag=3 : Stop at Tiny Step.</li> +<li>exitflag=4 : Solved To Acceptable Level.</li> +<li>exitflag=5 : Converged to a point of local infeasibility.</li></ul></p> + <p class="para">For more details on exitflag see the ipopt documentation, go to http://www.coin-or.org/Ipopt/documentation/</p> + <p class="para">The output data structure contains detailed informations about the optimization process. +It has type "struct" and contains the following fields. +<ul class="itemizedlist"><li>output.Iterations: The number of iterations performed during the search</li> +<li>output.Cpu_Time: The total cpu-time spend during the search</li> +<li>output.Objective_Evaluation: The number of Objective Evaluations performed during the search</li> +<li>output.Dual_Infeasibility: The Dual Infeasiblity of the final soution</li></ul></p> + <p class="para">The lambda data structure contains the Lagrange multipliers at the end +of optimization. In the current version the values are returned only when the the solution is optimal. +It has type "struct" and contains the following fields. +<ul class="itemizedlist"><li>lambda.lower: The Lagrange multipliers for the lower bound constraints.</li> +<li>lambda.upper: The Lagrange multipliers for the upper bound constraints.</li> +<li>lambda.eqlin: The Lagrange multipliers for the linear equality constraints.</li> +<li>lambda.ineqlin: The Lagrange multipliers for the linear inequality constraints.</li> +<li>lambda.eqnonlin: The Lagrange multipliers for the non-linear equality constraints.</li> +<li>lambda.ineqnonlin: The Lagrange multipliers for the non-linear inequality constraints.</li></ul></p> + <p class="para"></p></div> + +<div class="refsection"><h3 class="title">Examples</h3> + <div class="programlisting"><table border="0" width="100%"><tr><td width="98%"><pre class="scilabcode"><span class="scilabcomment">//Find x in R^2 such that it minimizes:</span> +<span class="scilabcomment">//f(x)= -x1 -x2/3</span> +<span class="scilabcomment">//x0=[0,0]</span> +<span class="scilabcomment">//constraint-1 (c1): x1 + x2 </span><span class="scilabcomment"><</span><span class="scilabcomment">= 2</span> +<span class="scilabcomment">//constraint-2 (c2): x1 + x2/4 </span><span class="scilabcomment"><</span><span class="scilabcomment">= 1</span> +<span class="scilabcomment">//constraint-3 (c3): x1 - x2 </span><span class="scilabcomment"><</span><span class="scilabcomment">= 2</span> +<span class="scilabcomment">//constraint-4 (c4): -x1/4 - x2 </span><span class="scilabcomment"><</span><span class="scilabcomment">= 1</span> +<span class="scilabcomment">//constraint-5 (c5): -x1 - x2 </span><span class="scilabcomment"><</span><span class="scilabcomment">= -1</span> +<span class="scilabcomment">//constraint-6 (c6): -x1 + x2 </span><span class="scilabcomment"><</span><span class="scilabcomment">= 2</span> +<span class="scilabcomment">//constraint-7 (c7): x1 + x2 = 2</span> +<span class="scilabcomment">//Objective function to be minimised</span> +<span class="scilabfkeyword">function</span> <span class="scilabinputoutputargs">y</span><span class="scilaboperator">=</span><span class="scilabfunctionid">f</span><span class="scilabopenclose">(</span><span class="scilabinputoutputargs">x</span><span class="scilabopenclose">)</span> +<span class="scilabinputoutputargs">y</span><span class="scilaboperator">=</span><span class="scilaboperator">-</span><span class="scilabinputoutputargs">x</span><span class="scilabopenclose">(</span><span class="scilabnumber">1</span><span class="scilabopenclose">)</span><span class="scilaboperator">-</span><span class="scilabinputoutputargs">x</span><span class="scilabopenclose">(</span><span class="scilabnumber">2</span><span class="scilabopenclose">)</span><span class="scilaboperator">/</span><span class="scilabnumber">3</span><span class="scilabdefault">;</span> +<span class="scilabfkeyword">endfunction</span> +<span class="scilabcomment">//Starting point, linear constraints and variable bounds</span> +<span class="scilabid">x0</span><span class="scilaboperator">=</span><span class="scilabopenclose">[</span><span class="scilabnumber">0</span> <span class="scilabdefault">,</span> <span class="scilabnumber">0</span><span class="scilabopenclose">]</span><span class="scilabdefault">;</span> +<span class="scilabid">A</span><span class="scilaboperator">=</span><span class="scilabopenclose">[</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilabnumber">1</span> <span class="scilabdefault">;</span> <span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilabnumber">1</span><span class="scilaboperator">/</span><span class="scilabnumber">4</span> <span class="scilabdefault">;</span> <span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilaboperator">-</span><span class="scilabnumber">1</span> <span class="scilabdefault">;</span> <span class="scilaboperator">-</span><span class="scilabnumber">1</span><span class="scilaboperator">/</span><span class="scilabnumber">4</span><span class="scilabdefault">,</span><span class="scilaboperator">-</span><span class="scilabnumber">1</span> <span class="scilabdefault">;</span> <span class="scilaboperator">-</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilaboperator">-</span><span class="scilabnumber">1</span> <span class="scilabdefault">;</span> <span class="scilaboperator">-</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilabnumber">1</span><span class="scilabopenclose">]</span><span class="scilabdefault">;</span> +<span class="scilabid">b</span><span class="scilaboperator">=</span><span class="scilabopenclose">[</span><span class="scilabnumber">2</span><span class="scilabdefault">;</span><span class="scilabnumber">1</span><span class="scilabdefault">;</span><span class="scilabnumber">2</span><span class="scilabdefault">;</span><span class="scilabnumber">1</span><span class="scilabdefault">;</span><span class="scilaboperator">-</span><span class="scilabnumber">1</span><span class="scilabdefault">;</span><span class="scilabnumber">2</span><span class="scilabopenclose">]</span><span class="scilabdefault">;</span> +<span class="scilabid">Aeq</span><span class="scilaboperator">=</span><span class="scilabopenclose">[</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilabnumber">1</span><span class="scilabopenclose">]</span><span class="scilabdefault">;</span> +<span class="scilabid">beq</span><span class="scilaboperator">=</span><span class="scilabopenclose">[</span><span class="scilabnumber">2</span><span class="scilabopenclose">]</span><span class="scilabdefault">;</span> +<span class="scilabid">lb</span><span class="scilaboperator">=</span><span class="scilabopenclose">[</span><span class="scilabopenclose">]</span><span class="scilabdefault">;</span> +<span class="scilabid">ub</span><span class="scilaboperator">=</span><span class="scilabopenclose">[</span><span class="scilabopenclose">]</span><span class="scilabdefault">;</span> +<span class="scilabid">nlc</span><span class="scilaboperator">=</span><span class="scilabopenclose">[</span><span class="scilabopenclose">]</span><span class="scilabdefault">;</span> +<span class="scilabcomment">//Gradient of objective function</span> +<span class="scilabfkeyword">function</span> <span class="scilabinputoutputargs">y</span><span class="scilaboperator">=</span><span class="scilabfunctionid">fGrad</span><span class="scilabopenclose">(</span><span class="scilabinputoutputargs">x</span><span class="scilabopenclose">)</span> +<span class="scilabinputoutputargs">y</span><span class="scilaboperator">=</span> <span class="scilabopenclose">[</span><span class="scilaboperator">-</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilaboperator">-</span><span class="scilabnumber">1</span><span class="scilaboperator">/</span><span class="scilabnumber">3</span><span class="scilabopenclose">]</span><span class="scilabdefault">;</span> +<span class="scilabfkeyword">endfunction</span> +<span class="scilabcomment">//Hessian of lagrangian</span> +<span class="scilabfkeyword">function</span> <span class="scilabinputoutputargs">y</span><span class="scilaboperator">=</span><span class="scilabfunctionid">lHess</span><span class="scilabopenclose">(</span><span class="scilabinputoutputargs">x</span><span class="scilabdefault">, </span><span class="scilabinputoutputargs">obj</span><span class="scilabdefault">, </span><span class="scilabinputoutputargs">lambda</span><span class="scilabopenclose">)</span> +<span class="scilabinputoutputargs">y</span><span class="scilaboperator">=</span> <span class="scilabinputoutputargs">obj</span><span class="scilaboperator">*</span><span class="scilabopenclose">[</span><span class="scilabnumber">0</span><span class="scilabdefault">,</span><span class="scilabnumber">0</span><span class="scilabdefault">;</span><span class="scilabnumber">0</span><span class="scilabdefault">,</span><span class="scilabnumber">0</span><span class="scilabopenclose">]</span> +<span class="scilabfkeyword">endfunction</span> +<span class="scilabcomment">//Options</span> +<span class="scilabid">options</span><span class="scilaboperator">=</span><a class="scilabcommand" href="scilab://list">list</a><span class="scilabopenclose">(</span><span class="scilabstring">"</span><span class="scilabstring">GradObj</span><span class="scilabstring">"</span><span class="scilabdefault">,</span> <span class="scilabfunctionid">fGrad</span><span class="scilabdefault">,</span> <span class="scilabstring">"</span><span class="scilabstring">Hessian</span><span class="scilabstring">"</span><span class="scilabdefault">,</span> <span class="scilabfunctionid">lHess</span><span class="scilabopenclose">)</span><span class="scilabdefault">;</span> +<span class="scilabcomment">//Calling Ipopt</span> +<span class="scilabopenclose">[</span><span class="scilabid">x</span><span class="scilabdefault">,</span><span class="scilabid">fval</span><span class="scilabdefault">,</span><span class="scilabid">exitflag</span><span class="scilabdefault">,</span><span class="scilabid">output</span><span class="scilabdefault">,</span><span class="scilabid">lambda</span><span class="scilabdefault">,</span><span class="scilabid">grad</span><span class="scilabdefault">,</span><span class="scilabid">hessian</span><span class="scilabopenclose">]</span> <span class="scilaboperator">=</span><span class="scilabid">fmincon</span><span class="scilabopenclose">(</span><span class="scilabfunctionid">f</span><span class="scilabdefault">,</span> <span class="scilabid">x0</span><span class="scilabdefault">,</span><span class="scilabid">A</span><span class="scilabdefault">,</span><span class="scilabid">b</span><span class="scilabdefault">,</span><span class="scilabid">Aeq</span><span class="scilabdefault">,</span><span class="scilabid">beq</span><span class="scilabdefault">,</span><span class="scilabid">lb</span><span class="scilabdefault">,</span><span class="scilabid">ub</span><span class="scilabdefault">,</span><span class="scilabid">nlc</span><span class="scilabdefault">,</span><span class="scilabid">options</span><span class="scilabopenclose">)</span></pre></td><td valign="top"><a href="scilab://scilab.execexample/"><img src="ScilabExecute.png" border="0"/></a></td><td valign="top"><a href="scilab://scilab.editexample/"><img src="ScilabEdit.png" border="0"/></a></td><td></td></tr></table></div></div> + +<div class="refsection"><h3 class="title">Examples</h3> + <div class="programlisting"><table border="0" width="100%"><tr><td width="98%"><pre class="scilabcode"><span class="scilabcomment">//Find x in R^3 such that it minimizes:</span> +<span class="scilabcomment">//f(x)= x1*x2 + x2*x3</span> +<span class="scilabcomment">//x0=[0.1 , 0.1 , 0.1]</span> +<span class="scilabcomment">//constraint-1 (c1): x1^2 - x2^2 + x3^2 </span><span class="scilabcomment"><</span><span class="scilabcomment">= 2</span> +<span class="scilabcomment">//constraint-2 (c2): x1^2 + x2^2 + x3^2 </span><span class="scilabcomment"><</span><span class="scilabcomment">= 10</span> +<span class="scilabcomment">//Objective function to be minimised</span> +<span class="scilabfkeyword">function</span> <span class="scilabinputoutputargs">y</span><span class="scilaboperator">=</span><span class="scilabfunctionid">f</span><span class="scilabopenclose">(</span><span class="scilabinputoutputargs">x</span><span class="scilabopenclose">)</span> +<span class="scilabinputoutputargs">y</span><span class="scilaboperator">=</span><span class="scilabinputoutputargs">x</span><span class="scilabopenclose">(</span><span class="scilabnumber">1</span><span class="scilabopenclose">)</span><span class="scilaboperator">*</span><span class="scilabinputoutputargs">x</span><span class="scilabopenclose">(</span><span class="scilabnumber">2</span><span class="scilabopenclose">)</span><span class="scilaboperator">+</span><span class="scilabinputoutputargs">x</span><span class="scilabopenclose">(</span><span class="scilabnumber">2</span><span class="scilabopenclose">)</span><span class="scilaboperator">*</span><span class="scilabinputoutputargs">x</span><span class="scilabopenclose">(</span><span class="scilabnumber">3</span><span class="scilabopenclose">)</span><span class="scilabdefault">;</span> +<span class="scilabfkeyword">endfunction</span> +<span class="scilabcomment">//Starting point, linear constraints and variable bounds</span> +<span class="scilabid">x0</span><span class="scilaboperator">=</span><span class="scilabopenclose">[</span><span class="scilabnumber">0.1</span> <span class="scilabdefault">,</span> <span class="scilabnumber">0.1</span> <span class="scilabdefault">,</span> <span class="scilabnumber">0.1</span><span class="scilabopenclose">]</span><span class="scilabdefault">;</span> +<span class="scilabid">A</span><span class="scilaboperator">=</span><span class="scilabopenclose">[</span><span class="scilabopenclose">]</span><span class="scilabdefault">;</span> +<span class="scilabid">b</span><span class="scilaboperator">=</span><span class="scilabopenclose">[</span><span class="scilabopenclose">]</span><span class="scilabdefault">;</span> +<span class="scilabid">Aeq</span><span class="scilaboperator">=</span><span class="scilabopenclose">[</span><span class="scilabopenclose">]</span><span class="scilabdefault">;</span> +<span class="scilabid">beq</span><span class="scilaboperator">=</span><span class="scilabopenclose">[</span><span class="scilabopenclose">]</span><span class="scilabdefault">;</span> +<span class="scilabid">lb</span><span class="scilaboperator">=</span><span class="scilabopenclose">[</span><span class="scilabopenclose">]</span><span class="scilabdefault">;</span> +<span class="scilabid">ub</span><span class="scilaboperator">=</span><span class="scilabopenclose">[</span><span class="scilabopenclose">]</span><span class="scilabdefault">;</span> +<span class="scilabcomment">//Nonlinear constraints</span> +<span class="scilabfkeyword">function</span> <span class="scilabopenclose">[</span><span class="scilabinputoutputargs">c</span><span class="scilabdefault">, </span><span class="scilabinputoutputargs">ceq</span><span class="scilabopenclose">]</span><span class="scilaboperator">=</span><span class="scilabfunctionid">nlc</span><span class="scilabopenclose">(</span><span class="scilabinputoutputargs">x</span><span class="scilabopenclose">)</span> +<span class="scilabinputoutputargs">c</span> <span class="scilaboperator">=</span> <span class="scilabopenclose">[</span><span class="scilabinputoutputargs">x</span><span class="scilabopenclose">(</span><span class="scilabnumber">1</span><span class="scilabopenclose">)</span><span class="scilaboperator">^</span><span class="scilabnumber">2</span> <span class="scilaboperator">-</span> <span class="scilabinputoutputargs">x</span><span class="scilabopenclose">(</span><span class="scilabnumber">2</span><span class="scilabopenclose">)</span><span class="scilaboperator">^</span><span class="scilabnumber">2</span> <span class="scilaboperator">+</span> <span class="scilabinputoutputargs">x</span><span class="scilabopenclose">(</span><span class="scilabnumber">3</span><span class="scilabopenclose">)</span><span class="scilaboperator">^</span><span class="scilabnumber">2</span> <span class="scilaboperator">-</span> <span class="scilabnumber">2</span> <span class="scilabdefault">,</span> <span class="scilabinputoutputargs">x</span><span class="scilabopenclose">(</span><span class="scilabnumber">1</span><span class="scilabopenclose">)</span><span class="scilaboperator">^</span><span class="scilabnumber">2</span> <span class="scilaboperator">+</span> <span class="scilabinputoutputargs">x</span><span class="scilabopenclose">(</span><span class="scilabnumber">2</span><span class="scilabopenclose">)</span><span class="scilaboperator">^</span><span class="scilabnumber">2</span> <span class="scilaboperator">+</span> <span class="scilabinputoutputargs">x</span><span class="scilabopenclose">(</span><span class="scilabnumber">3</span><span class="scilabopenclose">)</span><span class="scilaboperator">^</span><span class="scilabnumber">2</span> <span class="scilaboperator">-</span> <span class="scilabnumber">10</span><span class="scilabopenclose">]</span><span class="scilabdefault">;</span> +<span class="scilabinputoutputargs">ceq</span> <span class="scilaboperator">=</span> <span class="scilabopenclose">[</span><span class="scilabopenclose">]</span><span class="scilabdefault">;</span> +<span class="scilabfkeyword">endfunction</span> +<span class="scilabcomment">//Gradient of objective function</span> +<span class="scilabfkeyword">function</span> <span class="scilabinputoutputargs">y</span><span class="scilaboperator">=</span><span class="scilabfunctionid">fGrad</span><span class="scilabopenclose">(</span><span class="scilabinputoutputargs">x</span><span class="scilabopenclose">)</span> +<span class="scilabinputoutputargs">y</span><span class="scilaboperator">=</span> <span class="scilabopenclose">[</span><span class="scilabinputoutputargs">x</span><span class="scilabopenclose">(</span><span class="scilabnumber">2</span><span class="scilabopenclose">)</span><span class="scilabdefault">,</span><span class="scilabinputoutputargs">x</span><span class="scilabopenclose">(</span><span class="scilabnumber">1</span><span class="scilabopenclose">)</span><span class="scilaboperator">+</span><span class="scilabinputoutputargs">x</span><span class="scilabopenclose">(</span><span class="scilabnumber">3</span><span class="scilabopenclose">)</span><span class="scilabdefault">,</span><span class="scilabinputoutputargs">x</span><span class="scilabopenclose">(</span><span class="scilabnumber">2</span><span class="scilabopenclose">)</span><span class="scilabopenclose">]</span><span class="scilabdefault">;</span> +<span class="scilabfkeyword">endfunction</span> +<span class="scilabcomment">//Hessian of the Lagrange Function</span> +<span class="scilabfkeyword">function</span> <span class="scilabinputoutputargs">y</span><span class="scilaboperator">=</span><span class="scilabfunctionid">lHess</span><span class="scilabopenclose">(</span><span class="scilabinputoutputargs">x</span><span class="scilabdefault">, </span><span class="scilabinputoutputargs">obj</span><span class="scilabdefault">, </span><span class="scilabinputoutputargs">lambda</span><span class="scilabopenclose">)</span> +<span class="scilabinputoutputargs">y</span><span class="scilaboperator">=</span> <span class="scilabinputoutputargs">obj</span><span class="scilaboperator">*</span><span class="scilabopenclose">[</span><span class="scilabnumber">0</span><span class="scilabdefault">,</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilabnumber">0</span><span class="scilabdefault">;</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilabnumber">0</span><span class="scilabdefault">,</span><span class="scilabnumber">1</span><span class="scilabdefault">;</span><span class="scilabnumber">0</span><span class="scilabdefault">,</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilabnumber">0</span><span class="scilabopenclose">]</span> <span class="scilaboperator">+</span> <span class="scilabinputoutputargs">lambda</span><span class="scilabopenclose">(</span><span class="scilabnumber">1</span><span class="scilabopenclose">)</span><span class="scilaboperator">*</span><span class="scilabopenclose">[</span><span class="scilabnumber">2</span><span class="scilabdefault">,</span><span class="scilabnumber">0</span><span class="scilabdefault">,</span><span class="scilabnumber">0</span><span class="scilabdefault">;</span><span class="scilabnumber">0</span><span class="scilabdefault">,</span><span class="scilaboperator">-</span><span class="scilabnumber">2</span><span class="scilabdefault">,</span><span class="scilabnumber">0</span><span class="scilabdefault">;</span><span class="scilabnumber">0</span><span class="scilabdefault">,</span><span class="scilabnumber">0</span><span class="scilabdefault">,</span><span class="scilabnumber">2</span><span class="scilabopenclose">]</span> <span class="scilaboperator">+</span> <span class="scilabinputoutputargs">lambda</span><span class="scilabopenclose">(</span><span class="scilabnumber">2</span><span class="scilabopenclose">)</span><span class="scilaboperator">*</span><span class="scilabopenclose">[</span><span class="scilabnumber">2</span><span class="scilabdefault">,</span><span class="scilabnumber">0</span><span class="scilabdefault">,</span><span class="scilabnumber">0</span><span class="scilabdefault">;</span><span class="scilabnumber">0</span><span class="scilabdefault">,</span><span class="scilabnumber">2</span><span class="scilabdefault">,</span><span class="scilabnumber">0</span><span class="scilabdefault">;</span><span class="scilabnumber">0</span><span class="scilabdefault">,</span><span class="scilabnumber">0</span><span class="scilabdefault">,</span><span class="scilabnumber">2</span><span class="scilabopenclose">]</span> +<span class="scilabfkeyword">endfunction</span> +<span class="scilabcomment">//Gradient of Non-Linear Constraints</span> +<span class="scilabfkeyword">function</span> <span class="scilabopenclose">[</span><span class="scilabinputoutputargs">cg</span><span class="scilabdefault">, </span><span class="scilabinputoutputargs">ceqg</span><span class="scilabopenclose">]</span><span class="scilaboperator">=</span><span class="scilabfunctionid">cGrad</span><span class="scilabopenclose">(</span><span class="scilabinputoutputargs">x</span><span class="scilabopenclose">)</span> +<span class="scilabinputoutputargs">cg</span><span class="scilaboperator">=</span><span class="scilabopenclose">[</span><span class="scilabnumber">2</span><span class="scilaboperator">*</span><span class="scilabinputoutputargs">x</span><span class="scilabopenclose">(</span><span class="scilabnumber">1</span><span class="scilabopenclose">)</span> <span class="scilabdefault">,</span> <span class="scilaboperator">-</span><span class="scilabnumber">2</span><span class="scilaboperator">*</span><span class="scilabinputoutputargs">x</span><span class="scilabopenclose">(</span><span class="scilabnumber">2</span><span class="scilabopenclose">)</span> <span class="scilabdefault">,</span> <span class="scilabnumber">2</span><span class="scilaboperator">*</span><span class="scilabinputoutputargs">x</span><span class="scilabopenclose">(</span><span class="scilabnumber">3</span><span class="scilabopenclose">)</span> <span class="scilabdefault">;</span> <span class="scilabnumber">2</span><span class="scilaboperator">*</span><span class="scilabinputoutputargs">x</span><span class="scilabopenclose">(</span><span class="scilabnumber">1</span><span class="scilabopenclose">)</span> <span class="scilabdefault">,</span> <span class="scilabnumber">2</span><span class="scilaboperator">*</span><span class="scilabinputoutputargs">x</span><span class="scilabopenclose">(</span><span class="scilabnumber">2</span><span class="scilabopenclose">)</span> <span class="scilabdefault">,</span> <span class="scilabnumber">2</span><span class="scilaboperator">*</span><span class="scilabinputoutputargs">x</span><span class="scilabopenclose">(</span><span class="scilabnumber">3</span><span class="scilabopenclose">)</span><span class="scilabopenclose">]</span><span class="scilabdefault">;</span> +<span class="scilabinputoutputargs">ceqg</span><span class="scilaboperator">=</span><span class="scilabopenclose">[</span><span class="scilabopenclose">]</span><span class="scilabdefault">;</span> +<span class="scilabfkeyword">endfunction</span> +<span class="scilabcomment">//Options</span> +<span class="scilabid">options</span><span class="scilaboperator">=</span><a class="scilabcommand" href="scilab://list">list</a><span class="scilabopenclose">(</span><span class="scilabstring">"</span><span class="scilabstring">MaxIter</span><span class="scilabstring">"</span><span class="scilabdefault">,</span> <span class="scilabopenclose">[</span><span class="scilabnumber">1500</span><span class="scilabopenclose">]</span><span class="scilabdefault">,</span> <span class="scilabstring">"</span><span class="scilabstring">CpuTime</span><span class="scilabstring">"</span><span class="scilabdefault">,</span> <span class="scilabopenclose">[</span><span class="scilabnumber">500</span><span class="scilabopenclose">]</span><span class="scilabdefault">,</span> <span class="scilabstring">"</span><span class="scilabstring">GradObj</span><span class="scilabstring">"</span><span class="scilabdefault">,</span> <span class="scilabfunctionid">fGrad</span><span class="scilabdefault">,</span> <span class="scilabstring">"</span><span class="scilabstring">Hessian</span><span class="scilabstring">"</span><span class="scilabdefault">,</span> <span class="scilabfunctionid">lHess</span><span class="scilabdefault">,</span><span class="scilabstring">"</span><span class="scilabstring">GradCon</span><span class="scilabstring">"</span><span class="scilabdefault">,</span> <span class="scilabfunctionid">cGrad</span><span class="scilabopenclose">)</span><span class="scilabdefault">;</span> +<span class="scilabcomment">//Calling Ipopt</span> +<span class="scilabopenclose">[</span><span class="scilabid">x</span><span class="scilabdefault">,</span><span class="scilabid">fval</span><span class="scilabdefault">,</span><span class="scilabid">exitflag</span><span class="scilabdefault">,</span><span class="scilabid">output</span><span class="scilabopenclose">]</span> <span class="scilaboperator">=</span><span class="scilabid">fmincon</span><span class="scilabopenclose">(</span><span class="scilabfunctionid">f</span><span class="scilabdefault">,</span> <span class="scilabid">x0</span><span class="scilabdefault">,</span><span class="scilabid">A</span><span class="scilabdefault">,</span><span class="scilabid">b</span><span class="scilabdefault">,</span><span class="scilabid">Aeq</span><span class="scilabdefault">,</span><span class="scilabid">beq</span><span class="scilabdefault">,</span><span class="scilabid">lb</span><span class="scilabdefault">,</span><span class="scilabid">ub</span><span class="scilabdefault">,</span><span class="scilabfunctionid">nlc</span><span class="scilabdefault">,</span><span class="scilabid">options</span><span class="scilabopenclose">)</span></pre></td><td valign="top"><a href="scilab://scilab.execexample/"><img src="ScilabExecute.png" border="0"/></a></td><td valign="top"><a href="scilab://scilab.editexample/"><img src="ScilabEdit.png" border="0"/></a></td><td></td></tr></table></div></div> + +<div class="refsection"><h3 class="title">Examples</h3> + <div class="programlisting"><table border="0" width="100%"><tr><td width="98%"><pre class="scilabcode"><span class="scilabcomment">//The below problem is an unbounded problem:</span> +<span class="scilabcomment">//Find x in R^3 such that it minimizes:</span> +<span class="scilabcomment">//f(x)= -(x1^2 + x2^2 + x3^2)</span> +<span class="scilabcomment">//x0=[0.1 , 0.1 , 0.1]</span> +<span class="scilabcomment">// x1 </span><span class="scilabcomment"><</span><span class="scilabcomment">= 0</span> +<span class="scilabcomment">// x2 </span><span class="scilabcomment"><</span><span class="scilabcomment">= 0</span> +<span class="scilabcomment">// x3 </span><span class="scilabcomment"><</span><span class="scilabcomment">= 0</span> +<span class="scilabcomment">//Objective function to be minimised</span> +<span class="scilabfkeyword">function</span> <span class="scilabinputoutputargs">y</span><span class="scilaboperator">=</span><span class="scilabfunctionid">f</span><span class="scilabopenclose">(</span><span class="scilabinputoutputargs">x</span><span class="scilabopenclose">)</span> +<span class="scilabinputoutputargs">y</span><span class="scilaboperator">=</span><span class="scilaboperator">-</span><span class="scilabopenclose">(</span><span class="scilabinputoutputargs">x</span><span class="scilabopenclose">(</span><span class="scilabnumber">1</span><span class="scilabopenclose">)</span><span class="scilaboperator">^</span><span class="scilabnumber">2</span><span class="scilaboperator">+</span><span class="scilabinputoutputargs">x</span><span class="scilabopenclose">(</span><span class="scilabnumber">2</span><span class="scilabopenclose">)</span><span class="scilaboperator">^</span><span class="scilabnumber">2</span><span class="scilaboperator">+</span><span class="scilabinputoutputargs">x</span><span class="scilabopenclose">(</span><span class="scilabnumber">3</span><span class="scilabopenclose">)</span><span class="scilaboperator">^</span><span class="scilabnumber">2</span><span class="scilabopenclose">)</span><span class="scilabdefault">;</span> +<span class="scilabfkeyword">endfunction</span> +<span class="scilabcomment">//Starting point, linear constraints and variable bounds</span> +<span class="scilabid">x0</span><span class="scilaboperator">=</span><span class="scilabopenclose">[</span><span class="scilabnumber">0.1</span> <span class="scilabdefault">,</span> <span class="scilabnumber">0.1</span> <span class="scilabdefault">,</span> <span class="scilabnumber">0.1</span><span class="scilabopenclose">]</span><span class="scilabdefault">;</span> +<span class="scilabid">A</span><span class="scilaboperator">=</span><span class="scilabopenclose">[</span><span class="scilabopenclose">]</span><span class="scilabdefault">;</span> +<span class="scilabid">b</span><span class="scilaboperator">=</span><span class="scilabopenclose">[</span><span class="scilabopenclose">]</span><span class="scilabdefault">;</span> +<span class="scilabid">Aeq</span><span class="scilaboperator">=</span><span class="scilabopenclose">[</span><span class="scilabopenclose">]</span><span class="scilabdefault">;</span> +<span class="scilabid">beq</span><span class="scilaboperator">=</span><span class="scilabopenclose">[</span><span class="scilabopenclose">]</span><span class="scilabdefault">;</span> +<span class="scilabid">lb</span><span class="scilaboperator">=</span><span class="scilabopenclose">[</span><span class="scilabopenclose">]</span><span class="scilabdefault">;</span> +<span class="scilabid">ub</span><span class="scilaboperator">=</span><span class="scilabopenclose">[</span><span class="scilabnumber">0</span><span class="scilabdefault">,</span><span class="scilabnumber">0</span><span class="scilabdefault">,</span><span class="scilabnumber">0</span><span class="scilabopenclose">]</span><span class="scilabdefault">;</span> +<span class="scilabcomment">//Options</span> +<span class="scilabid">options</span><span class="scilaboperator">=</span><a class="scilabcommand" href="scilab://list">list</a><span class="scilabopenclose">(</span><span class="scilabstring">"</span><span class="scilabstring">MaxIter</span><span class="scilabstring">"</span><span class="scilabdefault">,</span> <span class="scilabopenclose">[</span><span class="scilabnumber">1500</span><span class="scilabopenclose">]</span><span class="scilabdefault">,</span> <span class="scilabstring">"</span><span class="scilabstring">CpuTime</span><span class="scilabstring">"</span><span class="scilabdefault">,</span> <span class="scilabopenclose">[</span><span class="scilabnumber">500</span><span class="scilabopenclose">]</span><span class="scilabopenclose">)</span><span class="scilabdefault">;</span> +<span class="scilabcomment">//Calling Ipopt</span> +<span class="scilabopenclose">[</span><span class="scilabid">x</span><span class="scilabdefault">,</span><span class="scilabid">fval</span><span class="scilabdefault">,</span><span class="scilabid">exitflag</span><span class="scilabdefault">,</span><span class="scilabid">output</span><span class="scilabdefault">,</span><span class="scilabid">lambda</span><span class="scilabdefault">,</span><span class="scilabid">grad</span><span class="scilabdefault">,</span><span class="scilabid">hessian</span><span class="scilabopenclose">]</span> <span class="scilaboperator">=</span><span class="scilabid">fmincon</span><span class="scilabopenclose">(</span><span class="scilabfunctionid">f</span><span class="scilabdefault">,</span> <span class="scilabid">x0</span><span class="scilabdefault">,</span><span class="scilabid">A</span><span class="scilabdefault">,</span><span class="scilabid">b</span><span class="scilabdefault">,</span><span class="scilabid">Aeq</span><span class="scilabdefault">,</span><span class="scilabid">beq</span><span class="scilabdefault">,</span><span class="scilabid">lb</span><span class="scilabdefault">,</span><span class="scilabid">ub</span><span class="scilabdefault">,</span><span class="scilabopenclose">[</span><span class="scilabopenclose">]</span><span class="scilabdefault">,</span><span class="scilabid">options</span><span class="scilabopenclose">)</span></pre></td><td valign="top"><a href="scilab://scilab.execexample/"><img src="ScilabExecute.png" border="0"/></a></td><td valign="top"><a href="scilab://scilab.editexample/"><img src="ScilabEdit.png" border="0"/></a></td><td></td></tr></table></div></div> + +<div class="refsection"><h3 class="title">Examples</h3> + <div class="programlisting"><table border="0" width="100%"><tr><td width="98%"><pre class="scilabcode"><span class="scilabcomment">//The below problem is an infeasible problem:</span> +<span class="scilabcomment">//Find x in R^3 such that in minimizes:</span> +<span class="scilabcomment">//f(x)=x1*x2 + x2*x3</span> +<span class="scilabcomment">//x0=[1,1,1]</span> +<span class="scilabcomment">//constraint-1 (c1): x1^2 </span><span class="scilabcomment"><</span><span class="scilabcomment">= 1</span> +<span class="scilabcomment">//constraint-2 (c2): x1^2 + x2^2 </span><span class="scilabcomment"><</span><span class="scilabcomment">= 1</span> +<span class="scilabcomment">//constraint-3 (c3): x3^2 </span><span class="scilabcomment"><</span><span class="scilabcomment">= 1</span> +<span class="scilabcomment">//constraint-4 (c4): x1^3 = 0.5</span> +<span class="scilabcomment">//constraint-5 (c5): x2^2 + x3^2 = 0.75</span> +<span class="scilabcomment">// 0 </span><span class="scilabcomment"><</span><span class="scilabcomment">= x1 </span><span class="scilabcomment"><</span><span class="scilabcomment">=0.6</span> +<span class="scilabcomment">// 0.2 </span><span class="scilabcomment"><</span><span class="scilabcomment">= x2 </span><span class="scilabcomment"><</span><span class="scilabcomment">= inf</span> +<span class="scilabcomment">// -inf </span><span class="scilabcomment"><</span><span class="scilabcomment">= x3 </span><span class="scilabcomment"><</span><span class="scilabcomment">= 1</span> +<span class="scilabcomment">//Objective function to be minimised</span> +<span class="scilabfkeyword">function</span> <span class="scilabinputoutputargs">y</span><span class="scilaboperator">=</span><span class="scilabfunctionid">f</span><span class="scilabopenclose">(</span><span class="scilabinputoutputargs">x</span><span class="scilabopenclose">)</span> +<span class="scilabinputoutputargs">y</span><span class="scilaboperator">=</span><span class="scilabinputoutputargs">x</span><span class="scilabopenclose">(</span><span class="scilabnumber">1</span><span class="scilabopenclose">)</span><span class="scilaboperator">*</span><span class="scilabinputoutputargs">x</span><span class="scilabopenclose">(</span><span class="scilabnumber">2</span><span class="scilabopenclose">)</span><span class="scilaboperator">+</span><span class="scilabinputoutputargs">x</span><span class="scilabopenclose">(</span><span class="scilabnumber">2</span><span class="scilabopenclose">)</span><span class="scilaboperator">*</span><span class="scilabinputoutputargs">x</span><span class="scilabopenclose">(</span><span class="scilabnumber">3</span><span class="scilabopenclose">)</span><span class="scilabdefault">;</span> +<span class="scilabfkeyword">endfunction</span> +<span class="scilabcomment">//Starting point, linear constraints and variable bounds</span> +<span class="scilabid">x0</span><span class="scilaboperator">=</span><span class="scilabopenclose">[</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilabnumber">1</span><span class="scilabopenclose">]</span><span class="scilabdefault">;</span> +<span class="scilabid">A</span><span class="scilaboperator">=</span><span class="scilabopenclose">[</span><span class="scilabopenclose">]</span><span class="scilabdefault">;</span> +<span class="scilabid">b</span><span class="scilaboperator">=</span><span class="scilabopenclose">[</span><span class="scilabopenclose">]</span><span class="scilabdefault">;</span> +<span class="scilabid">Aeq</span><span class="scilaboperator">=</span><span class="scilabopenclose">[</span><span class="scilabopenclose">]</span><span class="scilabdefault">;</span> +<span class="scilabid">beq</span><span class="scilaboperator">=</span><span class="scilabopenclose">[</span><span class="scilabopenclose">]</span><span class="scilabdefault">;</span> +<span class="scilabid">lb</span><span class="scilaboperator">=</span><span class="scilabopenclose">[</span><span class="scilabnumber">0</span> <span class="scilabnumber">0.2</span><span class="scilabdefault">,</span><span class="scilaboperator">-</span><span class="scilabconstants">%inf</span><span class="scilabopenclose">]</span><span class="scilabdefault">;</span> +<span class="scilabid">ub</span><span class="scilaboperator">=</span><span class="scilabopenclose">[</span><span class="scilabnumber">0.6</span> <span class="scilabconstants">%inf</span><span class="scilabdefault">,</span><span class="scilabnumber">1</span><span class="scilabopenclose">]</span><span class="scilabdefault">;</span> +<span class="scilabcomment">//Nonlinear constraints</span> +<span class="scilabfkeyword">function</span> <span class="scilabopenclose">[</span><span class="scilabinputoutputargs">c</span><span class="scilabdefault">, </span><span class="scilabinputoutputargs">ceq</span><span class="scilabopenclose">]</span><span class="scilaboperator">=</span><span class="scilabfunctionid">nlc</span><span class="scilabopenclose">(</span><span class="scilabinputoutputargs">x</span><span class="scilabopenclose">)</span> +<span class="scilabinputoutputargs">c</span><span class="scilaboperator">=</span><span class="scilabopenclose">[</span><span class="scilabinputoutputargs">x</span><span class="scilabopenclose">(</span><span class="scilabnumber">1</span><span class="scilabopenclose">)</span><span class="scilaboperator">^</span><span class="scilabnumber">2</span><span class="scilaboperator">-</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilabinputoutputargs">x</span><span class="scilabopenclose">(</span><span class="scilabnumber">1</span><span class="scilabopenclose">)</span><span class="scilaboperator">^</span><span class="scilabnumber">2</span><span class="scilaboperator">+</span><span class="scilabinputoutputargs">x</span><span class="scilabopenclose">(</span><span class="scilabnumber">2</span><span class="scilabopenclose">)</span><span class="scilaboperator">^</span><span class="scilabnumber">2</span><span class="scilaboperator">-</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilabinputoutputargs">x</span><span class="scilabopenclose">(</span><span class="scilabnumber">3</span><span class="scilabopenclose">)</span><span class="scilaboperator">^</span><span class="scilabnumber">2</span><span class="scilaboperator">-</span><span class="scilabnumber">1</span><span class="scilabopenclose">]</span><span class="scilabdefault">;</span> +<span class="scilabinputoutputargs">ceq</span><span class="scilaboperator">=</span><span class="scilabopenclose">[</span><span class="scilabinputoutputargs">x</span><span class="scilabopenclose">(</span><span class="scilabnumber">1</span><span class="scilabopenclose">)</span><span class="scilaboperator">^</span><span class="scilabnumber">3</span><span class="scilaboperator">-</span><span class="scilabnumber">0.5</span><span class="scilabdefault">,</span><span class="scilabinputoutputargs">x</span><span class="scilabopenclose">(</span><span class="scilabnumber">2</span><span class="scilabopenclose">)</span><span class="scilaboperator">^</span><span class="scilabnumber">2</span><span class="scilaboperator">+</span><span class="scilabinputoutputargs">x</span><span class="scilabopenclose">(</span><span class="scilabnumber">3</span><span class="scilabopenclose">)</span><span class="scilaboperator">^</span><span class="scilabnumber">2</span><span class="scilaboperator">-</span><span class="scilabnumber">0.75</span><span class="scilabopenclose">]</span><span class="scilabdefault">;</span> +<span class="scilabfkeyword">endfunction</span> +<span class="scilabcomment">//Gradient of objective function</span> +<span class="scilabfkeyword">function</span> <span class="scilabinputoutputargs">y</span><span class="scilaboperator">=</span><span class="scilabfunctionid">fGrad</span><span class="scilabopenclose">(</span><span class="scilabinputoutputargs">x</span><span class="scilabopenclose">)</span> +<span class="scilabinputoutputargs">y</span><span class="scilaboperator">=</span> <span class="scilabopenclose">[</span><span class="scilabinputoutputargs">x</span><span class="scilabopenclose">(</span><span class="scilabnumber">2</span><span class="scilabopenclose">)</span><span class="scilabdefault">,</span><span class="scilabinputoutputargs">x</span><span class="scilabopenclose">(</span><span class="scilabnumber">1</span><span class="scilabopenclose">)</span><span class="scilaboperator">+</span><span class="scilabinputoutputargs">x</span><span class="scilabopenclose">(</span><span class="scilabnumber">3</span><span class="scilabopenclose">)</span><span class="scilabdefault">,</span><span class="scilabinputoutputargs">x</span><span class="scilabopenclose">(</span><span class="scilabnumber">2</span><span class="scilabopenclose">)</span><span class="scilabopenclose">]</span><span class="scilabdefault">;</span> +<span class="scilabfkeyword">endfunction</span> +<span class="scilabcomment">//Hessian of the Lagrange Function</span> +<span class="scilabfkeyword">function</span> <span class="scilabinputoutputargs">y</span><span class="scilaboperator">=</span><span class="scilabfunctionid">lHess</span><span class="scilabopenclose">(</span><span class="scilabinputoutputargs">x</span><span class="scilabdefault">, </span><span class="scilabinputoutputargs">obj</span><span class="scilabdefault">, </span><span class="scilabinputoutputargs">lambda</span><span class="scilabopenclose">)</span> +<span class="scilabinputoutputargs">y</span><span class="scilaboperator">=</span> <span class="scilabinputoutputargs">obj</span><span class="scilaboperator">*</span><span class="scilabopenclose">[</span><span class="scilabnumber">0</span><span class="scilabdefault">,</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilabnumber">0</span><span class="scilabdefault">;</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilabnumber">0</span><span class="scilabdefault">,</span><span class="scilabnumber">1</span><span class="scilabdefault">;</span><span class="scilabnumber">0</span><span class="scilabdefault">,</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilabnumber">0</span><span class="scilabopenclose">]</span> <span class="scilaboperator">+</span> <span class="scilabinputoutputargs">lambda</span><span class="scilabopenclose">(</span><span class="scilabnumber">1</span><span class="scilabopenclose">)</span><span class="scilaboperator">*</span><span class="scilabopenclose">[</span><span class="scilabnumber">2</span><span class="scilabdefault">,</span><span class="scilabnumber">0</span><span class="scilabdefault">,</span><span class="scilabnumber">0</span><span class="scilabdefault">;</span><span class="scilabnumber">0</span><span class="scilabdefault">,</span><span class="scilabnumber">0</span><span class="scilabdefault">,</span><span class="scilabnumber">0</span><span class="scilabdefault">;</span><span class="scilabnumber">0</span><span class="scilabdefault">,</span><span class="scilabnumber">0</span><span class="scilabdefault">,</span><span class="scilabnumber">0</span><span class="scilabopenclose">]</span> <span class="scilaboperator">+</span> <span class="scilabinputoutputargs">lambda</span><span class="scilabopenclose">(</span><span class="scilabnumber">2</span><span class="scilabopenclose">)</span><span class="scilaboperator">*</span><span class="scilabopenclose">[</span><span class="scilabnumber">2</span><span class="scilabdefault">,</span><span class="scilabnumber">0</span><span class="scilabdefault">,</span><span class="scilabnumber">0</span><span class="scilabdefault">;</span><span class="scilabnumber">0</span><span class="scilabdefault">,</span><span class="scilabnumber">2</span><span class="scilabdefault">,</span><span class="scilabnumber">0</span><span class="scilabdefault">;</span><span class="scilabnumber">0</span><span class="scilabdefault">,</span><span class="scilabnumber">0</span><span class="scilabdefault">,</span><span class="scilabnumber">0</span><span class="scilabopenclose">]</span> <span class="scilaboperator">+</span><span class="scilabinputoutputargs">lambda</span><span class="scilabopenclose">(</span><span class="scilabnumber">3</span><span class="scilabopenclose">)</span><span class="scilaboperator">*</span><span class="scilabopenclose">[</span><span class="scilabnumber">0</span><span class="scilabdefault">,</span><span class="scilabnumber">0</span><span class="scilabdefault">,</span><span class="scilabnumber">0</span><span class="scilabdefault">;</span><span class="scilabnumber">0</span><span class="scilabdefault">,</span><span class="scilabnumber">0</span><span class="scilabdefault">,</span><span class="scilabnumber">0</span><span class="scilabdefault">;</span><span class="scilabnumber">0</span><span class="scilabdefault">,</span><span class="scilabnumber">0</span><span class="scilabdefault">,</span><span class="scilabnumber">2</span><span class="scilabopenclose">]</span> <span class="scilaboperator">+</span> <span class="scilabinputoutputargs">lambda</span><span class="scilabopenclose">(</span><span class="scilabnumber">4</span><span class="scilabopenclose">)</span><span class="scilaboperator">*</span><span class="scilabopenclose">[</span><span class="scilabnumber">6</span><span class="scilaboperator">*</span><span class="scilabinputoutputargs">x</span><span class="scilabopenclose">(</span><span class="scilabnumber">1</span> <span class="scilabopenclose">)</span><span class="scilabdefault">,</span><span class="scilabnumber">0</span><span class="scilabdefault">,</span><span class="scilabnumber">0</span><span class="scilabdefault">;</span><span class="scilabnumber">0</span><span class="scilabdefault">,</span><span class="scilabnumber">0</span><span class="scilabdefault">,</span><span class="scilabnumber">0</span><span class="scilabdefault">;</span><span class="scilabnumber">0</span><span class="scilabdefault">,</span><span class="scilabnumber">0</span><span class="scilabdefault">,</span><span class="scilabnumber">0</span><span class="scilabopenclose">]</span> <span class="scilaboperator">+</span> <span class="scilabinputoutputargs">lambda</span><span class="scilabopenclose">(</span><span class="scilabnumber">5</span><span class="scilabopenclose">)</span><span class="scilaboperator">*</span><span class="scilabopenclose">[</span><span class="scilabnumber">0</span><span class="scilabdefault">,</span><span class="scilabnumber">0</span><span class="scilabdefault">,</span><span class="scilabnumber">0</span><span class="scilabdefault">;</span><span class="scilabnumber">0</span><span class="scilabdefault">,</span><span class="scilabnumber">2</span><span class="scilabdefault">,</span><span class="scilabnumber">0</span><span class="scilabdefault">;</span><span class="scilabnumber">0</span><span class="scilabdefault">,</span><span class="scilabnumber">0</span><span class="scilabdefault">,</span><span class="scilabnumber">2</span><span class="scilabopenclose">]</span><span class="scilabdefault">;</span> +<span class="scilabfkeyword">endfunction</span> +<span class="scilabcomment">//Gradient of Non-Linear Constraints</span> +<span class="scilabfkeyword">function</span> <span class="scilabopenclose">[</span><span class="scilabinputoutputargs">cg</span><span class="scilabdefault">, </span><span class="scilabinputoutputargs">ceqg</span><span class="scilabopenclose">]</span><span class="scilaboperator">=</span><span class="scilabfunctionid">cGrad</span><span class="scilabopenclose">(</span><span class="scilabinputoutputargs">x</span><span class="scilabopenclose">)</span> +<span class="scilabinputoutputargs">cg</span> <span class="scilaboperator">=</span> <span class="scilabopenclose">[</span><span class="scilabnumber">2</span><span class="scilaboperator">*</span><span class="scilabinputoutputargs">x</span><span class="scilabopenclose">(</span><span class="scilabnumber">1</span><span class="scilabopenclose">)</span><span class="scilabdefault">,</span><span class="scilabnumber">0</span><span class="scilabdefault">,</span><span class="scilabnumber">0</span><span class="scilabdefault">;</span><span class="scilabnumber">2</span><span class="scilaboperator">*</span><span class="scilabinputoutputargs">x</span><span class="scilabopenclose">(</span><span class="scilabnumber">1</span><span class="scilabopenclose">)</span><span class="scilabdefault">,</span><span class="scilabnumber">2</span><span class="scilaboperator">*</span><span class="scilabinputoutputargs">x</span><span class="scilabopenclose">(</span><span class="scilabnumber">2</span><span class="scilabopenclose">)</span><span class="scilabdefault">,</span><span class="scilabnumber">0</span><span class="scilabdefault">;</span><span class="scilabnumber">0</span><span class="scilabdefault">,</span><span class="scilabnumber">0</span><span class="scilabdefault">,</span><span class="scilabnumber">2</span><span class="scilaboperator">*</span><span class="scilabinputoutputargs">x</span><span class="scilabopenclose">(</span><span class="scilabnumber">3</span><span class="scilabopenclose">)</span><span class="scilabopenclose">]</span><span class="scilabdefault">;</span> +<span class="scilabinputoutputargs">ceqg</span> <span class="scilaboperator">=</span> <span class="scilabopenclose">[</span><span class="scilabnumber">3</span><span class="scilaboperator">*</span><span class="scilabinputoutputargs">x</span><span class="scilabopenclose">(</span><span class="scilabnumber">1</span><span class="scilabopenclose">)</span><span class="scilaboperator">^</span><span class="scilabnumber">2</span><span class="scilabdefault">,</span><span class="scilabnumber">0</span><span class="scilabdefault">,</span><span class="scilabnumber">0</span><span class="scilabdefault">;</span><span class="scilabnumber">0</span><span class="scilabdefault">,</span><span class="scilabnumber">2</span><span class="scilaboperator">*</span><span class="scilabinputoutputargs">x</span><span class="scilabopenclose">(</span><span class="scilabnumber">2</span><span class="scilabopenclose">)</span><span class="scilabdefault">,</span><span class="scilabnumber">2</span><span class="scilaboperator">*</span><span class="scilabinputoutputargs">x</span><span class="scilabopenclose">(</span><span class="scilabnumber">3</span><span class="scilabopenclose">)</span><span class="scilabopenclose">]</span><span class="scilabdefault">;</span> +<span class="scilabfkeyword">endfunction</span> +<span class="scilabcomment">//Options</span> +<span class="scilabid">options</span><span class="scilaboperator">=</span><a class="scilabcommand" href="scilab://list">list</a><span class="scilabopenclose">(</span><span class="scilabstring">"</span><span class="scilabstring">MaxIter</span><span class="scilabstring">"</span><span class="scilabdefault">,</span> <span class="scilabopenclose">[</span><span class="scilabnumber">1500</span><span class="scilabopenclose">]</span><span class="scilabdefault">,</span> <span class="scilabstring">"</span><span class="scilabstring">CpuTime</span><span class="scilabstring">"</span><span class="scilabdefault">,</span> <span class="scilabopenclose">[</span><span class="scilabnumber">500</span><span class="scilabopenclose">]</span><span class="scilabdefault">,</span> <span class="scilabstring">"</span><span class="scilabstring">GradObj</span><span class="scilabstring">"</span><span class="scilabdefault">,</span> <span class="scilabfunctionid">fGrad</span><span class="scilabdefault">,</span> <span class="scilabstring">"</span><span class="scilabstring">Hessian</span><span class="scilabstring">"</span><span class="scilabdefault">,</span> <span class="scilabfunctionid">lHess</span><span class="scilabdefault">,</span><span class="scilabstring">"</span><span class="scilabstring">GradCon</span><span class="scilabstring">"</span><span class="scilabdefault">,</span> <span class="scilabfunctionid">cGrad</span><span class="scilabopenclose">)</span><span class="scilabdefault">;</span> +<span class="scilabcomment">//Calling Ipopt</span> +<span class="scilabopenclose">[</span><span class="scilabid">x</span><span class="scilabdefault">,</span><span class="scilabid">fval</span><span class="scilabdefault">,</span><span class="scilabid">exitflag</span><span class="scilabdefault">,</span><span class="scilabid">output</span><span class="scilabdefault">,</span><span class="scilabid">lambda</span><span class="scilabdefault">,</span><span class="scilabid">grad</span><span class="scilabdefault">,</span><span class="scilabid">hessian</span><span class="scilabopenclose">]</span> <span class="scilaboperator">=</span><span class="scilabid">fmincon</span><span class="scilabopenclose">(</span><span class="scilabfunctionid">f</span><span class="scilabdefault">,</span> <span class="scilabid">x0</span><span class="scilabdefault">,</span><span class="scilabid">A</span><span class="scilabdefault">,</span><span class="scilabid">b</span><span class="scilabdefault">,</span><span class="scilabid">Aeq</span><span class="scilabdefault">,</span><span class="scilabid">beq</span><span class="scilabdefault">,</span><span class="scilabid">lb</span><span class="scilabdefault">,</span><span class="scilabid">ub</span><span class="scilabdefault">,</span><span class="scilabfunctionid">nlc</span><span class="scilabdefault">,</span><span class="scilabid">options</span><span class="scilabopenclose">)</span></pre></td><td valign="top"><a href="scilab://scilab.execexample/"><img src="ScilabExecute.png" border="0"/></a></td><td valign="top"><a href="scilab://scilab.editexample/"><img src="ScilabEdit.png" border="0"/></a></td><td></td></tr></table></div></div> + +<div class="refsection"><h3 class="title">Authors</h3> + <ul class="itemizedlist"><li class="member">R.Vidyadhar , Vignesh Kannan</li></ul></div> + <br /> + + <div class="manualnavbar"> + <table width="100%"> + <tr><td colspan="3" class="next"><a href="http://bugzilla.scilab.org/enter_bug.cgi?product=Scilab%20software&component=Documentation%20pages" class="ulink">Report an issue</a></td></tr> +<tr> + <td width="30%"> + <span class="previous"><a href="fminbnd.html"><< fminbnd</a></span> + + </td> + <td width="40%" class="center"> + <span class="top"><a href="section_19f4f1e5726c01d683e8b82be0a7e910.html">Symphony Toolbox</a></span> + + </td> + <td width="30%" class="next"> + <span class="next"><a href="fminunc.html">fminunc >></a></span> + + </td> + </tr></table> + <hr /> + </div> + </body> +</html> diff --git a/help/en_US/scilab_en_US_help/fminunc.html b/help/en_US/scilab_en_US_help/fminunc.html new file mode 100644 index 0000000..97ffdbf --- /dev/null +++ b/help/en_US/scilab_en_US_help/fminunc.html @@ -0,0 +1,178 @@ +<html><head> + <meta http-equiv="Content-Type" content="text/html; charset=utf-8"> + <title>fminunc</title> + <style type="text/css" media="all"> + @import url("scilab_code.css"); + @import url("xml_code.css"); + @import url("c_code.css"); + @import url("style.css"); + </style> + </head> + <body> + <div class="manualnavbar"> + <table width="100%"><tr> + <td width="30%"> + <span class="previous"><a href="fmincon.html"><< fmincon</a></span> + + </td> + <td width="40%" class="center"> + <span class="top"><a href="section_19f4f1e5726c01d683e8b82be0a7e910.html">Symphony Toolbox</a></span> + + </td> + <td width="30%" class="next"> + <span class="next"><a href="linprog.html">linprog >></a></span> + + </td> + </tr></table> + <hr /> + </div> + + + + <span class="path"><a href="index.html">Symphony Toolbox</a> >> <a href="section_19f4f1e5726c01d683e8b82be0a7e910.html">Symphony Toolbox</a> > fminunc</span> + + <br /><br /> + <div class="refnamediv"><h1 class="refname">fminunc</h1> + <p class="refpurpose">Solves a multi-variable unconstrainted optimization problem</p></div> + + +<div class="refsynopsisdiv"><h3 class="title">Calling Sequence</h3> + <div class="synopsis"><pre><span class="default">xopt</span><span class="default"> = </span><span class="functionid">fminunc</span><span class="default">(</span><span class="default">f</span><span class="default">,</span><span class="default">x0</span><span class="default">)</span> +<span class="default">xopt</span><span class="default"> = </span><span class="functionid">fminunc</span><span class="default">(</span><span class="default">f</span><span class="default">,</span><span class="default">x0</span><span class="default">,</span><span class="default">options</span><span class="default">)</span> +<span class="default">[</span><span class="default">xopt</span><span class="default">,</span><span class="default">fopt</span><span class="default">] = </span><span class="functionid">fminunc</span><span class="default">(.....)</span> +<span class="default">[</span><span class="default">xopt</span><span class="default">,</span><span class="default">fopt</span><span class="default">,</span><span class="default">exitflag</span><span class="default">]= </span><span class="functionid">fminunc</span><span class="default">(.....)</span> +<span class="default">[</span><span class="default">xopt</span><span class="default">,</span><span class="default">fopt</span><span class="default">,</span><span class="default">exitflag</span><span class="default">,</span><span class="default">output</span><span class="default">]= </span><span class="functionid">fminunc</span><span class="default">(.....)</span> +<span class="default">[</span><span class="default">xopt</span><span class="default">,</span><span class="default">fopt</span><span class="default">,</span><span class="default">exitflag</span><span class="default">,</span><span class="default">output</span><span class="default">,</span><span class="default">gradient</span><span class="default">]=</span><span class="functionid">fminunc</span><span class="default">(.....)</span> +<span class="default">[</span><span class="default">xopt</span><span class="default">,</span><span class="default">fopt</span><span class="default">,</span><span class="default">exitflag</span><span class="default">,</span><span class="default">output</span><span class="default">,</span><span class="default">gradient</span><span class="default">,</span><span class="default">hessian</span><span class="default">]=</span><span class="functionid">fminunc</span><span class="default">(.....)</span></pre></div></div> + +<div class="refsection"><h3 class="title">Parameters</h3> + <dl><dt><span class="term">f :</span> + <dd><p class="para">a function, representing the objective function of the problem</p></dd></dt> + <dt><span class="term">x0 :</span> + <dd><p class="para">a vector of doubles, containing the starting of variables.</p></dd></dt> + <dt><span class="term">options:</span> + <dd><p class="para">a list, containing the option for user to specify. See below for details.</p></dd></dt> + <dt><span class="term">xopt :</span> + <dd><p class="para">a vector of doubles, the computed solution of the optimization problem.</p></dd></dt> + <dt><span class="term">fopt :</span> + <dd><p class="para">a scalar of double, the function value at x.</p></dd></dt> + <dt><span class="term">exitflag :</span> + <dd><p class="para">a scalar of integer, containing the flag which denotes the reason for termination of algorithm. See below for details.</p></dd></dt> + <dt><span class="term">output :</span> + <dd><p class="para">a structure, containing the information about the optimization. See below for details.</p></dd></dt> + <dt><span class="term">gradient :</span> + <dd><p class="para">a vector of doubles, containing the the gradient of the solution.</p></dd></dt> + <dt><span class="term">hessian :</span> + <dd><p class="para">a matrix of doubles, containing the the hessian of the solution.</p></dd></dt></dl></div> + +<div class="refsection"><h3 class="title">Description</h3> + <p class="para">Search the minimum of an unconstrained optimization problem specified by : +Find the minimum of f(x) such that</p> + <p class="para"><span><img src='./_LaTeX_fminunc.xml_1.png' style='position:relative;top:9px;width:115px;height:26px'/></span></p> + <p class="para">The routine calls Ipopt for solving the Un-constrained Optimization problem, Ipopt is a library written in C++.</p> + <p class="para">The options allows the user to set various parameters of the Optimization problem. +It should be defined as type "list" and contains the following fields. +<ul class="itemizedlist"><li>Syntax : options= list("MaxIter", [---], "CpuTime", [---], "Gradient", ---, "Hessian", ---);</li> +<li>MaxIter : a Scalar, containing the Maximum Number of Iteration that the solver should take.</li> +<li>CpuTime : a Scalar, containing the Maximum amount of CPU Time that the solver should take.</li> +<li>Gradient : a function, representing the gradient function of the Objective in Vector Form.</li> +<li>Hessian : a function, representing the hessian function of the Objective in Symmetric Matrix Form.</li> +<li>Default Values : options = list("MaxIter", [3000], "CpuTime", [600]);</li></ul></p> + <p class="para">The exitflag allows to know the status of the optimization which is given back by Ipopt. +<ul class="itemizedlist"><li>exitflag=0 : Optimal Solution Found</li> +<li>exitflag=1 : Maximum Number of Iterations Exceeded. Output may not be optimal.</li> +<li>exitflag=2 : Maximum CPU Time exceeded. Output may not be optimal.</li> +<li>exitflag=3 : Stop at Tiny Step.</li> +<li>exitflag=4 : Solved To Acceptable Level.</li> +<li>exitflag=5 : Converged to a point of local infeasibility.</li></ul></p> + <p class="para">For more details on exitflag see the ipopt documentation, go to http://www.coin-or.org/Ipopt/documentation/</p> + <p class="para">The output data structure contains detailed informations about the optimization process. +It has type "struct" and contains the following fields. +<ul class="itemizedlist"><li>output.Iterations: The number of iterations performed during the search</li> +<li>output.Cpu_Time: The total cpu-time spend during the search</li> +<li>output.Objective_Evaluation: The number of Objective Evaluations performed during the search</li> +<li>output.Dual_Infeasibility: The Dual Infeasiblity of the final soution</li></ul></p> + <p class="para"></p></div> + +<div class="refsection"><h3 class="title">Examples</h3> + <div class="programlisting"><table border="0" width="100%"><tr><td width="98%"><pre class="scilabcode"><span class="scilabcomment">//Find x in R^2 such that it minimizes the Rosenbrock function</span> +<span class="scilabcomment">//f = 100*(x2 - x1^2)^2 + (1-x1)^2</span> +<span class="scilabcomment">//Objective function to be minimised</span> +<span class="scilabfkeyword">function</span> <span class="scilabinputoutputargs">y</span><span class="scilaboperator">=</span><span class="scilabfunctionid">f</span><span class="scilabopenclose">(</span><span class="scilabinputoutputargs">x</span><span class="scilabopenclose">)</span> +<span class="scilabinputoutputargs">y</span><span class="scilaboperator">=</span> <span class="scilabnumber">100</span><span class="scilaboperator">*</span><span class="scilabopenclose">(</span><span class="scilabinputoutputargs">x</span><span class="scilabopenclose">(</span><span class="scilabnumber">2</span><span class="scilabopenclose">)</span> <span class="scilaboperator">-</span> <span class="scilabinputoutputargs">x</span><span class="scilabopenclose">(</span><span class="scilabnumber">1</span><span class="scilabopenclose">)</span><span class="scilaboperator">^</span><span class="scilabnumber">2</span><span class="scilabopenclose">)</span><span class="scilaboperator">^</span><span class="scilabnumber">2</span> <span class="scilaboperator">+</span> <span class="scilabopenclose">(</span><span class="scilabnumber">1</span><span class="scilaboperator">-</span><span class="scilabinputoutputargs">x</span><span class="scilabopenclose">(</span><span class="scilabnumber">1</span><span class="scilabopenclose">)</span><span class="scilabopenclose">)</span><span class="scilaboperator">^</span><span class="scilabnumber">2</span><span class="scilabdefault">;</span> +<span class="scilabfkeyword">endfunction</span> +<span class="scilabcomment">//Starting point</span> +<span class="scilabid">x0</span><span class="scilaboperator">=</span><span class="scilabopenclose">[</span><span class="scilaboperator">-</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilabnumber">2</span><span class="scilabopenclose">]</span><span class="scilabdefault">;</span> +<span class="scilabcomment">//Gradient of objective function</span> +<span class="scilabfkeyword">function</span> <span class="scilabinputoutputargs">y</span><span class="scilaboperator">=</span><span class="scilabfunctionid">fGrad</span><span class="scilabopenclose">(</span><span class="scilabinputoutputargs">x</span><span class="scilabopenclose">)</span> +<span class="scilabinputoutputargs">y</span><span class="scilaboperator">=</span> <span class="scilabopenclose">[</span><span class="scilaboperator">-</span><span class="scilabnumber">400</span><span class="scilaboperator">*</span><span class="scilabinputoutputargs">x</span><span class="scilabopenclose">(</span><span class="scilabnumber">1</span><span class="scilabopenclose">)</span><span class="scilaboperator">*</span><span class="scilabinputoutputargs">x</span><span class="scilabopenclose">(</span><span class="scilabnumber">2</span><span class="scilabopenclose">)</span> <span class="scilaboperator">+</span> <span class="scilabnumber">400</span><span class="scilaboperator">*</span><span class="scilabinputoutputargs">x</span><span class="scilabopenclose">(</span><span class="scilabnumber">1</span><span class="scilabopenclose">)</span><span class="scilaboperator">^</span><span class="scilabnumber">3</span> <span class="scilaboperator">+</span> <span class="scilabnumber">2</span><span class="scilaboperator">*</span><span class="scilabinputoutputargs">x</span><span class="scilabopenclose">(</span><span class="scilabnumber">1</span><span class="scilabopenclose">)</span><span class="scilaboperator">-</span><span class="scilabnumber">2</span><span class="scilabdefault">,</span> <span class="scilabnumber">200</span><span class="scilaboperator">*</span><span class="scilabopenclose">(</span><span class="scilabinputoutputargs">x</span><span class="scilabopenclose">(</span><span class="scilabnumber">2</span><span class="scilabopenclose">)</span><span class="scilaboperator">-</span><span class="scilabinputoutputargs">x</span><span class="scilabopenclose">(</span><span class="scilabnumber">1</span><span class="scilabopenclose">)</span><span class="scilaboperator">^</span><span class="scilabnumber">2</span><span class="scilabopenclose">)</span><span class="scilabopenclose">]</span><span class="scilabdefault">;</span> +<span class="scilabfkeyword">endfunction</span> +<span class="scilabcomment">//Hessian of Objective Function</span> +<span class="scilabfkeyword">function</span> <span class="scilabinputoutputargs">y</span><span class="scilaboperator">=</span><span class="scilabfunctionid">fHess</span><span class="scilabopenclose">(</span><span class="scilabinputoutputargs">x</span><span class="scilabopenclose">)</span> +<span class="scilabinputoutputargs">y</span><span class="scilaboperator">=</span> <span class="scilabopenclose">[</span><span class="scilabnumber">1200</span><span class="scilaboperator">*</span><span class="scilabinputoutputargs">x</span><span class="scilabopenclose">(</span><span class="scilabnumber">1</span><span class="scilabopenclose">)</span><span class="scilaboperator">^</span><span class="scilabnumber">2</span><span class="scilaboperator">-</span> <span class="scilabnumber">400</span><span class="scilaboperator">*</span><span class="scilabinputoutputargs">x</span><span class="scilabopenclose">(</span><span class="scilabnumber">2</span><span class="scilabopenclose">)</span> <span class="scilaboperator">+</span> <span class="scilabnumber">2</span><span class="scilabdefault">,</span> <span class="scilaboperator">-</span><span class="scilabnumber">400</span><span class="scilaboperator">*</span><span class="scilabinputoutputargs">x</span><span class="scilabopenclose">(</span><span class="scilabnumber">1</span><span class="scilabopenclose">)</span><span class="scilabdefault">;</span><span class="scilaboperator">-</span><span class="scilabnumber">400</span><span class="scilaboperator">*</span><span class="scilabinputoutputargs">x</span><span class="scilabopenclose">(</span><span class="scilabnumber">1</span><span class="scilabopenclose">)</span><span class="scilabdefault">,</span> <span class="scilabnumber">200</span> <span class="scilabopenclose">]</span><span class="scilabdefault">;</span> +<span class="scilabfkeyword">endfunction</span> +<span class="scilabcomment">//Options</span> +<span class="scilabid">options</span><span class="scilaboperator">=</span><a class="scilabcommand" href="scilab://list">list</a><span class="scilabopenclose">(</span><span class="scilabstring">"</span><span class="scilabstring">MaxIter</span><span class="scilabstring">"</span><span class="scilabdefault">,</span> <span class="scilabopenclose">[</span><span class="scilabnumber">1500</span><span class="scilabopenclose">]</span><span class="scilabdefault">,</span> <span class="scilabstring">"</span><span class="scilabstring">CpuTime</span><span class="scilabstring">"</span><span class="scilabdefault">,</span> <span class="scilabopenclose">[</span><span class="scilabnumber">500</span><span class="scilabopenclose">]</span><span class="scilabdefault">,</span> <span class="scilabstring">"</span><span class="scilabstring">Gradient</span><span class="scilabstring">"</span><span class="scilabdefault">,</span> <span class="scilabfunctionid">fGrad</span><span class="scilabdefault">,</span> <span class="scilabstring">"</span><span class="scilabstring">Hessian</span><span class="scilabstring">"</span><span class="scilabdefault">,</span> <span class="scilabfunctionid">fHess</span><span class="scilabopenclose">)</span><span class="scilabdefault">;</span> +<span class="scilabcomment">//Calling Ipopt</span> +<span class="scilabopenclose">[</span><span class="scilabid">xopt</span><span class="scilabdefault">,</span><span class="scilabid">fopt</span><span class="scilabdefault">,</span><span class="scilabid">exitflag</span><span class="scilabdefault">,</span><span class="scilabid">output</span><span class="scilabdefault">,</span><span class="scilabid">gradient</span><span class="scilabdefault">,</span><span class="scilabid">hessian</span><span class="scilabopenclose">]</span><span class="scilaboperator">=</span><span class="scilabid">fminunc</span><span class="scilabopenclose">(</span><span class="scilabfunctionid">f</span><span class="scilabdefault">,</span><span class="scilabid">x0</span><span class="scilabdefault">,</span><span class="scilabid">options</span><span class="scilabopenclose">)</span></pre></td><td valign="top"><a href="scilab://scilab.execexample/"><img src="ScilabExecute.png" border="0"/></a></td><td valign="top"><a href="scilab://scilab.editexample/"><img src="ScilabEdit.png" border="0"/></a></td><td></td></tr></table></div></div> + +<div class="refsection"><h3 class="title">Examples</h3> + <div class="programlisting"><table border="0" width="100%"><tr><td width="98%"><pre class="scilabcode"><span class="scilabcomment">//Find x in R^2 such that the below function is minimum</span> +<span class="scilabcomment">//f = x1^2 + x2^2</span> +<span class="scilabcomment">//Objective function to be minimised</span> +<span class="scilabfkeyword">function</span> <span class="scilabinputoutputargs">y</span><span class="scilaboperator">=</span><span class="scilabfunctionid">f</span><span class="scilabopenclose">(</span><span class="scilabinputoutputargs">x</span><span class="scilabopenclose">)</span> +<span class="scilabinputoutputargs">y</span><span class="scilaboperator">=</span> <span class="scilabinputoutputargs">x</span><span class="scilabopenclose">(</span><span class="scilabnumber">1</span><span class="scilabopenclose">)</span><span class="scilaboperator">^</span><span class="scilabnumber">2</span> <span class="scilaboperator">+</span> <span class="scilabinputoutputargs">x</span><span class="scilabopenclose">(</span><span class="scilabnumber">2</span><span class="scilabopenclose">)</span><span class="scilaboperator">^</span><span class="scilabnumber">2</span><span class="scilabdefault">;</span> +<span class="scilabfkeyword">endfunction</span> +<span class="scilabcomment">//Starting point</span> +<span class="scilabid">x0</span><span class="scilaboperator">=</span><span class="scilabopenclose">[</span><span class="scilabnumber">2</span><span class="scilabdefault">,</span><span class="scilabnumber">1</span><span class="scilabopenclose">]</span><span class="scilabdefault">;</span> +<span class="scilabcomment">//Calling Ipopt</span> +<span class="scilabopenclose">[</span><span class="scilabid">xopt</span><span class="scilabdefault">,</span><span class="scilabid">fopt</span><span class="scilabopenclose">]</span><span class="scilaboperator">=</span><span class="scilabid">fminunc</span><span class="scilabopenclose">(</span><span class="scilabfunctionid">f</span><span class="scilabdefault">,</span><span class="scilabid">x0</span><span class="scilabopenclose">)</span></pre></td><td valign="top"><a href="scilab://scilab.execexample/"><img src="ScilabExecute.png" border="0"/></a></td><td valign="top"><a href="scilab://scilab.editexample/"><img src="ScilabEdit.png" border="0"/></a></td><td></td></tr></table></div></div> + +<div class="refsection"><h3 class="title">Examples</h3> + <div class="programlisting"><table border="0" width="100%"><tr><td width="98%"><pre class="scilabcode"><span class="scilabcomment">//The below problem is an unbounded problem:</span> +<span class="scilabcomment">//Find x in R^2 such that the below function is minimum</span> +<span class="scilabcomment">//f = - x1^2 - x2^2</span> +<span class="scilabcomment">//Objective function to be minimised</span> +<span class="scilabfkeyword">function</span> <span class="scilabinputoutputargs">y</span><span class="scilaboperator">=</span><span class="scilabfunctionid">f</span><span class="scilabopenclose">(</span><span class="scilabinputoutputargs">x</span><span class="scilabopenclose">)</span> +<span class="scilabinputoutputargs">y</span><span class="scilaboperator">=</span> <span class="scilaboperator">-</span><span class="scilabinputoutputargs">x</span><span class="scilabopenclose">(</span><span class="scilabnumber">1</span><span class="scilabopenclose">)</span><span class="scilaboperator">^</span><span class="scilabnumber">2</span> <span class="scilaboperator">-</span> <span class="scilabinputoutputargs">x</span><span class="scilabopenclose">(</span><span class="scilabnumber">2</span><span class="scilabopenclose">)</span><span class="scilaboperator">^</span><span class="scilabnumber">2</span><span class="scilabdefault">;</span> +<span class="scilabfkeyword">endfunction</span> +<span class="scilabcomment">//Starting point</span> +<span class="scilabid">x0</span><span class="scilaboperator">=</span><span class="scilabopenclose">[</span><span class="scilabnumber">2</span><span class="scilabdefault">,</span><span class="scilabnumber">1</span><span class="scilabopenclose">]</span><span class="scilabdefault">;</span> +<span class="scilabcomment">//Gradient of objective function</span> +<span class="scilabfkeyword">function</span> <span class="scilabinputoutputargs">y</span><span class="scilaboperator">=</span><span class="scilabfunctionid">fGrad</span><span class="scilabopenclose">(</span><span class="scilabinputoutputargs">x</span><span class="scilabopenclose">)</span> +<span class="scilabinputoutputargs">y</span><span class="scilaboperator">=</span> <span class="scilabopenclose">[</span><span class="scilaboperator">-</span><span class="scilabnumber">2</span><span class="scilaboperator">*</span><span class="scilabinputoutputargs">x</span><span class="scilabopenclose">(</span><span class="scilabnumber">1</span><span class="scilabopenclose">)</span><span class="scilabdefault">,</span><span class="scilaboperator">-</span><span class="scilabnumber">2</span><span class="scilaboperator">*</span><span class="scilabinputoutputargs">x</span><span class="scilabopenclose">(</span><span class="scilabnumber">2</span><span class="scilabopenclose">)</span><span class="scilabopenclose">]</span><span class="scilabdefault">;</span> +<span class="scilabfkeyword">endfunction</span> +<span class="scilabcomment">//Hessian of Objective Function</span> +<span class="scilabfkeyword">function</span> <span class="scilabinputoutputargs">y</span><span class="scilaboperator">=</span><span class="scilabfunctionid">fHess</span><span class="scilabopenclose">(</span><span class="scilabinputoutputargs">x</span><span class="scilabopenclose">)</span> +<span class="scilabinputoutputargs">y</span><span class="scilaboperator">=</span> <span class="scilabopenclose">[</span><span class="scilaboperator">-</span><span class="scilabnumber">2</span><span class="scilabdefault">,</span><span class="scilabnumber">0</span><span class="scilabdefault">;</span><span class="scilabnumber">0</span><span class="scilabdefault">,</span><span class="scilaboperator">-</span><span class="scilabnumber">2</span><span class="scilabopenclose">]</span><span class="scilabdefault">;</span> +<span class="scilabfkeyword">endfunction</span> +<span class="scilabcomment">//Options</span> +<span class="scilabid">options</span><span class="scilaboperator">=</span><a class="scilabcommand" href="scilab://list">list</a><span class="scilabopenclose">(</span><span class="scilabstring">"</span><span class="scilabstring">MaxIter</span><span class="scilabstring">"</span><span class="scilabdefault">,</span> <span class="scilabopenclose">[</span><span class="scilabnumber">1500</span><span class="scilabopenclose">]</span><span class="scilabdefault">,</span> <span class="scilabstring">"</span><span class="scilabstring">CpuTime</span><span class="scilabstring">"</span><span class="scilabdefault">,</span> <span class="scilabopenclose">[</span><span class="scilabnumber">500</span><span class="scilabopenclose">]</span><span class="scilabdefault">,</span> <span class="scilabstring">"</span><span class="scilabstring">Gradient</span><span class="scilabstring">"</span><span class="scilabdefault">,</span> <span class="scilabfunctionid">fGrad</span><span class="scilabdefault">,</span> <span class="scilabstring">"</span><span class="scilabstring">Hessian</span><span class="scilabstring">"</span><span class="scilabdefault">,</span> <span class="scilabfunctionid">fHess</span><span class="scilabopenclose">)</span><span class="scilabdefault">;</span> +<span class="scilabcomment">//Calling Ipopt</span> +<span class="scilabopenclose">[</span><span class="scilabid">xopt</span><span class="scilabdefault">,</span><span class="scilabid">fopt</span><span class="scilabdefault">,</span><span class="scilabid">exitflag</span><span class="scilabdefault">,</span><span class="scilabid">output</span><span class="scilabdefault">,</span><span class="scilabid">gradient</span><span class="scilabdefault">,</span><span class="scilabid">hessian</span><span class="scilabopenclose">]</span><span class="scilaboperator">=</span><span class="scilabid">fminunc</span><span class="scilabopenclose">(</span><span class="scilabfunctionid">f</span><span class="scilabdefault">,</span><span class="scilabid">x0</span><span class="scilabdefault">,</span><span class="scilabid">options</span><span class="scilabopenclose">)</span></pre></td><td valign="top"><a href="scilab://scilab.execexample/"><img src="ScilabExecute.png" border="0"/></a></td><td valign="top"><a href="scilab://scilab.editexample/"><img src="ScilabEdit.png" border="0"/></a></td><td></td></tr></table></div></div> + +<div class="refsection"><h3 class="title">Authors</h3> + <ul class="itemizedlist"><li class="member">R.Vidyadhar , Vignesh Kannan</li></ul></div> + <br /> + + <div class="manualnavbar"> + <table width="100%"> + <tr><td colspan="3" class="next"><a href="http://bugzilla.scilab.org/enter_bug.cgi?product=Scilab%20software&component=Documentation%20pages" class="ulink">Report an issue</a></td></tr> +<tr> + <td width="30%"> + <span class="previous"><a href="fmincon.html"><< fmincon</a></span> + + </td> + <td width="40%" class="center"> + <span class="top"><a href="section_19f4f1e5726c01d683e8b82be0a7e910.html">Symphony Toolbox</a></span> + + </td> + <td width="30%" class="next"> + <span class="next"><a href="linprog.html">linprog >></a></span> + + </td> + </tr></table> + <hr /> + </div> + </body> +</html> diff --git a/help/en_US/scilab_en_US_help/index.html b/help/en_US/scilab_en_US_help/index.html index 03ce98c..fc07de0 100644 --- a/help/en_US/scilab_en_US_help/index.html +++ b/help/en_US/scilab_en_US_help/index.html @@ -32,7 +32,37 @@ <ul class="list-part"><a name="symphony_toolbox_manual"></a><div class="info"></div> <li><a href="section_19f4f1e5726c01d683e8b82be0a7e910.html" class="part">Symphony Toolbox</a> -<ul class="list-chapter"><li><a href="lsqlin.html" class="refentry">lsqlin</a> — <span class="refentry-description">Solves a linear quadratic problem.</span></li> +<ul class="list-chapter"><li><a href="fgoalattain.html" class="refentry">fgoalattain</a> — <span class="refentry-description">Solves a multiobjective goal attainment problem</span></li> + + + + + +<li><a href="fminbnd.html" class="refentry">fminbnd</a> — <span class="refentry-description">Solves a multi-variable optimization problem on a bounded interval</span></li> + + + + + +<li><a href="fmincon.html" class="refentry">fmincon</a> — <span class="refentry-description">Solves a multi-variable constrainted optimization problem</span></li> + + + + + +<li><a href="fminunc.html" class="refentry">fminunc</a> — <span class="refentry-description">Solves a multi-variable unconstrainted optimization problem</span></li> + + + + + +<li><a href="linprog.html" class="refentry">linprog</a> — <span class="refentry-description">Solves a linear programming problem.</span></li> + + + + + +<li><a href="lsqlin.html" class="refentry">lsqlin</a> — <span class="refentry-description">Solves a linear quadratic problem.</span></li> diff --git a/help/en_US/scilab_en_US_help/jhelpmap.jhm b/help/en_US/scilab_en_US_help/jhelpmap.jhm index 0226c5e..be43c6e 100644 --- a/help/en_US/scilab_en_US_help/jhelpmap.jhm +++ b/help/en_US/scilab_en_US_help/jhelpmap.jhm @@ -3,6 +3,11 @@ <map version="1.0"> <mapID target="index" url="index.html"/> <mapID target="section_19f4f1e5726c01d683e8b82be0a7e910" url="section_19f4f1e5726c01d683e8b82be0a7e910.html"/> +<mapID target="fgoalattain" url="fgoalattain.html"/> +<mapID target="fminbnd" url="fminbnd.html"/> +<mapID target="fmincon" url="fmincon.html"/> +<mapID target="fminunc" url="fminunc.html"/> +<mapID target="linprog" url="linprog.html"/> <mapID target="lsqlin" url="lsqlin.html"/> <mapID target="lsqnonneg" url="lsqnonneg.html"/> <mapID target="qpipopt" url="qpipopt.html"/> diff --git a/help/en_US/scilab_en_US_help/jhelptoc.xml b/help/en_US/scilab_en_US_help/jhelptoc.xml index f53e713..500c6b0 100644 --- a/help/en_US/scilab_en_US_help/jhelptoc.xml +++ b/help/en_US/scilab_en_US_help/jhelptoc.xml @@ -3,6 +3,11 @@ <toc version="1.0"> <tocitem target="index" text="Symphony Toolbox"> <tocitem target="section_19f4f1e5726c01d683e8b82be0a7e910" text="Symphony Toolbox"> +<tocitem target="fgoalattain" text="fgoalattain"/> +<tocitem target="fminbnd" text="fminbnd"/> +<tocitem target="fmincon" text="fmincon"/> +<tocitem target="fminunc" text="fminunc"/> +<tocitem target="linprog" text="linprog"/> <tocitem target="lsqlin" text="lsqlin"/> <tocitem target="lsqnonneg" text="lsqnonneg"/> <tocitem target="qpipopt" text="qpipopt"/> diff --git a/help/en_US/scilab_en_US_help/linprog.html b/help/en_US/scilab_en_US_help/linprog.html new file mode 100644 index 0000000..260b8b3 --- /dev/null +++ b/help/en_US/scilab_en_US_help/linprog.html @@ -0,0 +1,188 @@ +<html><head> + <meta http-equiv="Content-Type" content="text/html; charset=utf-8"> + <title>linprog</title> + <style type="text/css" media="all"> + @import url("scilab_code.css"); + @import url("xml_code.css"); + @import url("c_code.css"); + @import url("style.css"); + </style> + </head> + <body> + <div class="manualnavbar"> + <table width="100%"><tr> + <td width="30%"> + <span class="previous"><a href="fminunc.html"><< fminunc</a></span> + + </td> + <td width="40%" class="center"> + <span class="top"><a href="section_19f4f1e5726c01d683e8b82be0a7e910.html">Symphony Toolbox</a></span> + + </td> + <td width="30%" class="next"> + <span class="next"><a href="lsqlin.html">lsqlin >></a></span> + + </td> + </tr></table> + <hr /> + </div> + + + + <span class="path"><a href="index.html">Symphony Toolbox</a> >> <a href="section_19f4f1e5726c01d683e8b82be0a7e910.html">Symphony Toolbox</a> > linprog</span> + + <br /><br /> + <div class="refnamediv"><h1 class="refname">linprog</h1> + <p class="refpurpose">Solves a linear programming problem.</p></div> + + +<div class="refsynopsisdiv"><h3 class="title">Calling Sequence</h3> + <div class="synopsis"><pre><span class="default">xopt</span><span class="default"> = </span><span class="functionid">linprog</span><span class="default">(</span><span class="default">c</span><span class="default">,</span><span class="default">A</span><span class="default">,</span><span class="default">b</span><span class="default">)</span> +<span class="default">xopt</span><span class="default"> = </span><span class="functionid">linprog</span><span class="default">(</span><span class="default">c</span><span class="default">,</span><span class="default">A</span><span class="default">,</span><span class="default">b</span><span class="default">,</span><span class="default">Aeq</span><span class="default">,</span><span class="default">beq</span><span class="default">)</span> +<span class="default">xopt</span><span class="default"> = </span><span class="functionid">linprog</span><span class="default">(</span><span class="default">c</span><span class="default">,</span><span class="default">A</span><span class="default">,</span><span class="default">b</span><span class="default">,</span><span class="default">Aeq</span><span class="default">,</span><span class="default">beq</span><span class="default">,</span><span class="default">lb</span><span class="default">,</span><span class="default">ub</span><span class="default">)</span> +<span class="default">xopt</span><span class="default"> = </span><span class="functionid">linprog</span><span class="default">(</span><span class="default">c</span><span class="default">,</span><span class="default">A</span><span class="default">,</span><span class="default">b</span><span class="default">,</span><span class="default">Aeq</span><span class="default">,</span><span class="default">beq</span><span class="default">,</span><span class="default">lb</span><span class="default">,</span><span class="default">ub</span><span class="default">,</span><span class="default">param</span><span class="default">)</span> +<span class="default">[</span><span class="default">xopt</span><span class="default">, </span><span class="default">fopt</span><span class="default">, </span><span class="default">exitflag</span><span class="default">, </span><span class="default">output</span><span class="default">, </span><span class="default">lambda</span><span class="default">] = </span><span class="functionid">linprog</span><span class="default">(</span><span class="default">file</span><span class="default">)</span> +<span class="default">[</span><span class="default">xopt</span><span class="default">,</span><span class="default">fopt</span><span class="default">,</span><span class="default">exitflag</span><span class="default">,</span><span class="default">output</span><span class="default">,</span><span class="default">lambda</span><span class="default">] = </span><span class="functionid">linprog</span><span class="default">( ... )</span></pre></div></div> + +<div class="refsection"><h3 class="title">Parameters</h3> + <dl><dt><span class="term">c :</span> + <dd><p class="para">a vector of double, contains coefficients of the variables in the objective</p></dd></dt> + <dt><span class="term">A :</span> + <dd><p class="para">a matrix of double, represents the linear coefficients in the inequality constraints A⋅x ≤ b.</p></dd></dt> + <dt><span class="term">b :</span> + <dd><p class="para">a vector of double, represents the linear coefficients in the inequality constraints A⋅x ≤ b.</p></dd></dt> + <dt><span class="term">Aeq :</span> + <dd><p class="para">a matrix of double, represents the linear coefficients in the equality constraints Aeq⋅x = beq.</p></dd></dt> + <dt><span class="term">beq :</span> + <dd><p class="para">a vector of double, represents the linear coefficients in the equality constraints Aeq⋅x = beq.</p></dd></dt> + <dt><span class="term">lb :</span> + <dd><p class="para">Lower bounds, specified as a vector or array of double. lb represents the lower bounds elementwise in lb ≤ x ≤ ub.</p></dd></dt> + <dt><span class="term">ub :</span> + <dd><p class="para">Upper bounds, specified as a vector or array of double. ub represents the upper bounds elementwise in lb ≤ x ≤ ub.</p></dd></dt> + <dt><span class="term">options :</span> + <dd><p class="para">a list containing the parameters to be set.</p></dd></dt> + <dt><span class="term">file :</span> + <dd><p class="para">a string describing the path to the mps file.</p></dd></dt> + <dt><span class="term">xopt :</span> + <dd><p class="para">a vector of double, the computed solution of the optimization problem.</p></dd></dt> + <dt><span class="term">fopt :</span> + <dd><p class="para">a double, the value of the function at x.</p></dd></dt> + <dt><span class="term">status :</span> + <dd><p class="para">status flag returned from symphony. See below for details.</p></dd></dt> + <dt><span class="term">output :</span> + <dd><p class="para">The output data structure contains detailed information about the optimization process. See below for details.</p></dd></dt> + <dt><span class="term">lambda :</span> + <dd><p class="para">The structure consist of the Lagrange multipliers at the solution of problem. See below for details.</p></dd></dt></dl></div> + +<div class="refsection"><h3 class="title">Description</h3> + <p class="para">OSI-CLP is used for solving the linear programming problems, OSI-CLP is a library written in C++. +Search the minimum of a constrained linear programming problem specified by :</p> + <p class="para"><span><img src='./_LaTeX_linprog.xml_1.png' style='position:relative;top:40px;width:212px;height:88px'/></span> +The routine calls Clp for solving the linear programming problem, Clp is a library written in C++.</p> + <p class="para">The exitflag allows to know the status of the optimization which is given back by Ipopt. +<ul class="itemizedlist"><li>exitflag=0 : Optimal Solution Found</li> +<li>exitflag=1 : Primal Infeasible</li> +<li>exitflag=2 : Dual Infeasible</li> +<li>exitflag=3 : Maximum Number of Iterations Exceeded. Output may not be optimal.</li> +<li>exitflag=4 : Solution Abandoned</li> +<li>exitflag=5 : Primal objective limit reached.</li> +<li>exitflag=6 : Dual objective limit reached.</li></ul></p> + <p class="para">For more details on exitflag see the ipopt documentation, go to http://www.coin-or.org/Ipopt/documentation/</p> + <p class="para">The output data structure contains detailed informations about the optimization process. +It has type "struct" and contains the following fields. +<ul class="itemizedlist"><li>output.iterations: The number of iterations performed during the search</li> +<li>output.constrviolation: The max-norm of the constraint violation.</li></ul></p> + <p class="para">The lambda data structure contains the Lagrange multipliers at the end +of optimization. In the current version the values are returned only when the the solution is optimal. +It has type "struct" and contains the following fields. +<ul class="itemizedlist"><li>lambda.lower: The Lagrange multipliers for the lower bound constraints.</li> +<li>lambda.upper: The Lagrange multipliers for the upper bound constraints.</li> +<li>lambda.eqlin: The Lagrange multipliers for the linear equality constraints.</li> +<li>lambda.ineqlin: The Lagrange multipliers for the linear inequality constraints.</li></ul></p> + <p class="para"></p></div> + +<div class="refsection"><h3 class="title">Examples</h3> + <div class="programlisting"><table border="0" width="100%"><tr><td width="98%"><pre class="scilabcode"><span class="scilabcomment">//Optimal problems</span> +<span class="scilabcomment">//Linear program, linear inequality constraints</span> +<span class="scilabid">c</span><span class="scilaboperator">=</span><span class="scilabopenclose">[</span><span class="scilaboperator">-</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilaboperator">-</span><span class="scilabnumber">1</span><span class="scilaboperator">/</span><span class="scilabnumber">3</span><span class="scilabopenclose">]</span><span class="scilaboperator">'</span> +<span class="scilabid">A</span><span class="scilaboperator">=</span><span class="scilabopenclose">[</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilabnumber">1</span><span class="scilabdefault">;</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilabnumber">1</span><span class="scilaboperator">/</span><span class="scilabnumber">4</span><span class="scilabdefault">;</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilaboperator">-</span><span class="scilabnumber">1</span><span class="scilabdefault">;</span><span class="scilaboperator">-</span><span class="scilabnumber">1</span><span class="scilaboperator">/</span><span class="scilabnumber">4</span><span class="scilabdefault">,</span><span class="scilaboperator">-</span><span class="scilabnumber">1</span><span class="scilabdefault">;</span><span class="scilaboperator">-</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilaboperator">-</span><span class="scilabnumber">1</span><span class="scilabdefault">;</span><span class="scilaboperator">-</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilabnumber">1</span><span class="scilabopenclose">]</span> +<span class="scilabid">b</span><span class="scilaboperator">=</span><span class="scilabopenclose">[</span><span class="scilabnumber">2</span><span class="scilabdefault">,</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilabnumber">2</span><span class="scilabdefault">,</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilaboperator">-</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilabnumber">2</span><span class="scilabopenclose">]</span> +<span class="scilabopenclose">[</span><span class="scilabid">xopt</span><span class="scilabdefault">,</span><span class="scilabid">fopt</span><span class="scilabdefault">,</span><span class="scilabid">exitflag</span><span class="scilabdefault">,</span><span class="scilabid">output</span><span class="scilabdefault">,</span><span class="scilabid">lambda</span><span class="scilabopenclose">]</span><span class="scilaboperator">=</span><span class="scilabid">linprog</span><span class="scilabopenclose">(</span><span class="scilabid">c</span><span class="scilabdefault">,</span> <span class="scilabid">A</span><span class="scilabdefault">,</span> <span class="scilabid">b</span><span class="scilabopenclose">)</span> +<span class="scilabcomment">// Press ENTER to continue</span></pre></td><td valign="top"><a href="scilab://scilab.execexample/"><img src="ScilabExecute.png" border="0"/></a></td><td valign="top"><a href="scilab://scilab.editexample/"><img src="ScilabEdit.png" border="0"/></a></td><td></td></tr></table></div></div> + +<div class="refsection"><h3 class="title">Examples</h3> + <div class="programlisting"><table border="0" width="100%"><tr><td width="98%"><pre class="scilabcode"><span class="scilabcomment">//Linear program with Linear Inequalities and Equalities`</span> +<span class="scilabid">c</span><span class="scilaboperator">=</span><span class="scilabopenclose">[</span><span class="scilaboperator">-</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilaboperator">-</span><span class="scilabnumber">1</span><span class="scilaboperator">/</span><span class="scilabnumber">3</span><span class="scilabopenclose">]</span><span class="scilaboperator">'</span> +<span class="scilabid">A</span><span class="scilaboperator">=</span><span class="scilabopenclose">[</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilabnumber">1</span><span class="scilabdefault">;</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilabnumber">1</span><span class="scilaboperator">/</span><span class="scilabnumber">4</span><span class="scilabdefault">;</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilaboperator">-</span><span class="scilabnumber">1</span><span class="scilabdefault">;</span><span class="scilaboperator">-</span><span class="scilabnumber">1</span><span class="scilaboperator">/</span><span class="scilabnumber">4</span><span class="scilabdefault">,</span><span class="scilaboperator">-</span><span class="scilabnumber">1</span><span class="scilabdefault">;</span><span class="scilaboperator">-</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilaboperator">-</span><span class="scilabnumber">1</span><span class="scilabdefault">;</span><span class="scilaboperator">-</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilabnumber">1</span><span class="scilabopenclose">]</span> +<span class="scilabid">b</span><span class="scilaboperator">=</span><span class="scilabopenclose">[</span><span class="scilabnumber">2</span><span class="scilabdefault">,</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilabnumber">2</span><span class="scilabdefault">,</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilaboperator">-</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilabnumber">2</span><span class="scilabopenclose">]</span> +<span class="scilabid">Aeq</span><span class="scilaboperator">=</span><span class="scilabopenclose">[</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilabnumber">1</span><span class="scilaboperator">/</span><span class="scilabnumber">4</span><span class="scilabopenclose">]</span> +<span class="scilabid">beq</span><span class="scilaboperator">=</span><span class="scilabopenclose">[</span><span class="scilabnumber">1</span><span class="scilaboperator">/</span><span class="scilabnumber">2</span><span class="scilabopenclose">]</span> +<span class="scilabopenclose">[</span><span class="scilabid">xopt</span><span class="scilabdefault">,</span><span class="scilabid">fopt</span><span class="scilabdefault">,</span><span class="scilabid">exitflag</span><span class="scilabdefault">,</span><span class="scilabid">output</span><span class="scilabdefault">,</span><span class="scilabid">lambda</span><span class="scilabopenclose">]</span><span class="scilaboperator">=</span><span class="scilabid">linprog</span><span class="scilabopenclose">(</span><span class="scilabid">c</span><span class="scilabdefault">,</span> <span class="scilabid">A</span><span class="scilabdefault">,</span> <span class="scilabid">b</span><span class="scilabdefault">,</span> <span class="scilabid">Aeq</span><span class="scilabdefault">,</span> <span class="scilabid">beq</span><span class="scilabopenclose">)</span> +<span class="scilabcomment">// Press ENTER to continue</span></pre></td><td valign="top"><a href="scilab://scilab.execexample/"><img src="ScilabExecute.png" border="0"/></a></td><td valign="top"><a href="scilab://scilab.editexample/"><img src="ScilabEdit.png" border="0"/></a></td><td></td></tr></table></div></div> + +<div class="refsection"><h3 class="title">Examples</h3> + <div class="programlisting"><table border="0" width="100%"><tr><td width="98%"><pre class="scilabcode"><span class="scilabcomment">//Linear program with all constraint types</span> +<span class="scilabid">c</span><span class="scilaboperator">=</span><span class="scilabopenclose">[</span><span class="scilaboperator">-</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilaboperator">-</span><span class="scilabnumber">1</span><span class="scilaboperator">/</span><span class="scilabnumber">3</span><span class="scilabopenclose">]</span><span class="scilaboperator">'</span> +<span class="scilabid">A</span><span class="scilaboperator">=</span><span class="scilabopenclose">[</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilabnumber">1</span><span class="scilabdefault">;</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilabnumber">1</span><span class="scilaboperator">/</span><span class="scilabnumber">4</span><span class="scilabdefault">;</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilaboperator">-</span><span class="scilabnumber">1</span><span class="scilabdefault">;</span><span class="scilaboperator">-</span><span class="scilabnumber">1</span><span class="scilaboperator">/</span><span class="scilabnumber">4</span><span class="scilabdefault">,</span><span class="scilaboperator">-</span><span class="scilabnumber">1</span><span class="scilabdefault">;</span><span class="scilaboperator">-</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilaboperator">-</span><span class="scilabnumber">1</span><span class="scilabdefault">;</span><span class="scilaboperator">-</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilabnumber">1</span><span class="scilabopenclose">]</span> +<span class="scilabid">b</span><span class="scilaboperator">=</span><span class="scilabopenclose">[</span><span class="scilabnumber">2</span><span class="scilabdefault">,</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilabnumber">2</span><span class="scilabdefault">,</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilaboperator">-</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilabnumber">2</span><span class="scilabopenclose">]</span> +<span class="scilabid">Aeq</span><span class="scilaboperator">=</span><span class="scilabopenclose">[</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilabnumber">1</span><span class="scilaboperator">/</span><span class="scilabnumber">4</span><span class="scilabopenclose">]</span> +<span class="scilabid">beq</span><span class="scilaboperator">=</span><span class="scilabopenclose">[</span><span class="scilabnumber">1</span><span class="scilaboperator">/</span><span class="scilabnumber">2</span><span class="scilabopenclose">]</span> +<span class="scilabid">lb</span><span class="scilaboperator">=</span><span class="scilabopenclose">[</span><span class="scilaboperator">-</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilaboperator">-</span><span class="scilabnumber">0.5</span><span class="scilabopenclose">]</span> +<span class="scilabid">ub</span><span class="scilaboperator">=</span><span class="scilabopenclose">[</span><span class="scilabnumber">1.5</span><span class="scilabdefault">,</span><span class="scilabnumber">1.25</span><span class="scilabopenclose">]</span> +<span class="scilabopenclose">[</span><span class="scilabid">xopt</span><span class="scilabdefault">,</span><span class="scilabid">fopt</span><span class="scilabdefault">,</span><span class="scilabid">exitflag</span><span class="scilabdefault">,</span><span class="scilabid">output</span><span class="scilabdefault">,</span><span class="scilabid">lambda</span><span class="scilabopenclose">]</span><span class="scilaboperator">=</span><span class="scilabid">linprog</span><span class="scilabopenclose">(</span><span class="scilabid">c</span><span class="scilabdefault">,</span> <span class="scilabid">A</span><span class="scilabdefault">,</span> <span class="scilabid">b</span><span class="scilabdefault">,</span> <span class="scilabid">Aeq</span><span class="scilabdefault">,</span> <span class="scilabid">beq</span><span class="scilabdefault">,</span> <span class="scilabid">lb</span><span class="scilabdefault">,</span> <span class="scilabid">ub</span><span class="scilabopenclose">)</span> +<span class="scilabcomment">// Press ENTER to continue</span></pre></td><td valign="top"><a href="scilab://scilab.execexample/"><img src="ScilabExecute.png" border="0"/></a></td><td valign="top"><a href="scilab://scilab.editexample/"><img src="ScilabEdit.png" border="0"/></a></td><td></td></tr></table></div></div> + +<div class="refsection"><h3 class="title">Examples</h3> + <div class="programlisting"><table border="0" width="100%"><tr><td width="98%"><pre class="scilabcode"><span class="scilabcomment">//Primal Infeasible Problem</span> +<span class="scilabid">c</span><span class="scilaboperator">=</span><span class="scilabopenclose">[</span><span class="scilaboperator">-</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilaboperator">-</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilaboperator">-</span><span class="scilabnumber">1</span><span class="scilabopenclose">]</span><span class="scilaboperator">'</span> +<span class="scilabid">A</span><span class="scilaboperator">=</span><span class="scilabopenclose">[</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilabnumber">2</span><span class="scilabdefault">,</span><span class="scilaboperator">-</span><span class="scilabnumber">1</span><span class="scilabopenclose">]</span> +<span class="scilabid">b</span><span class="scilaboperator">=</span><span class="scilabopenclose">[</span><span class="scilaboperator">-</span><span class="scilabnumber">4</span><span class="scilabopenclose">]</span> +<span class="scilabid">Aeq</span><span class="scilaboperator">=</span><span class="scilabopenclose">[</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilabnumber">5</span><span class="scilabdefault">,</span><span class="scilabnumber">3</span><span class="scilabdefault">;</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilabnumber">0</span><span class="scilabopenclose">]</span> +<span class="scilabid">beq</span><span class="scilaboperator">=</span><span class="scilabopenclose">[</span><span class="scilabnumber">10</span><span class="scilabdefault">,</span><span class="scilabnumber">100</span><span class="scilabopenclose">]</span> +<span class="scilabid">lb</span><span class="scilaboperator">=</span><span class="scilabopenclose">[</span><span class="scilabnumber">0</span><span class="scilabdefault">,</span><span class="scilabnumber">0</span><span class="scilabdefault">,</span><span class="scilabnumber">0</span><span class="scilabopenclose">]</span> +<span class="scilabid">ub</span><span class="scilaboperator">=</span><span class="scilabopenclose">[</span><span class="scilabconstants">%inf</span><span class="scilabdefault">,</span><span class="scilabconstants">%inf</span><span class="scilabdefault">,</span><span class="scilabconstants">%inf</span><span class="scilabopenclose">]</span> +<span class="scilabopenclose">[</span><span class="scilabid">xopt</span><span class="scilabdefault">,</span><span class="scilabid">fopt</span><span class="scilabdefault">,</span><span class="scilabid">exitflag</span><span class="scilabdefault">,</span><span class="scilabid">output</span><span class="scilabdefault">,</span><span class="scilabid">lambda</span><span class="scilabopenclose">]</span><span class="scilaboperator">=</span> <span class="scilabid">linprog</span><span class="scilabopenclose">(</span><span class="scilabid">c</span><span class="scilabdefault">,</span><span class="scilabid">A</span><span class="scilabdefault">,</span><span class="scilabid">b</span><span class="scilabdefault">,</span><span class="scilabid">Aeq</span><span class="scilabdefault">,</span><span class="scilabid">beq</span><span class="scilabdefault">,</span><span class="scilabid">lb</span><span class="scilabdefault">,</span><span class="scilabid">ub</span><span class="scilabopenclose">)</span> +<span class="scilabcomment">// Press ENTER to continue</span></pre></td><td valign="top"><a href="scilab://scilab.execexample/"><img src="ScilabExecute.png" border="0"/></a></td><td valign="top"><a href="scilab://scilab.editexample/"><img src="ScilabEdit.png" border="0"/></a></td><td></td></tr></table></div></div> + +<div class="refsection"><h3 class="title">Examples</h3> + <div class="programlisting"><table border="0" width="100%"><tr><td width="98%"><pre class="scilabcode"><span class="scilabcomment">//Dual Infeasible Problem</span> +<span class="scilabid">c</span><span class="scilaboperator">=</span><span class="scilabopenclose">[</span><span class="scilabnumber">3</span><span class="scilabdefault">,</span><span class="scilabnumber">5</span><span class="scilabdefault">,</span><span class="scilaboperator">-</span><span class="scilabnumber">7</span><span class="scilabopenclose">]</span><span class="scilaboperator">'</span> +<span class="scilabid">A</span><span class="scilaboperator">=</span><span class="scilabopenclose">[</span><span class="scilaboperator">-</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilaboperator">-</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilabnumber">4</span><span class="scilabdefault">;</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilabnumber">4</span><span class="scilabopenclose">]</span> +<span class="scilabid">b</span><span class="scilaboperator">=</span><span class="scilabopenclose">[</span><span class="scilaboperator">-</span><span class="scilabnumber">8</span><span class="scilabdefault">,</span><span class="scilabnumber">5</span><span class="scilabopenclose">]</span> +<span class="scilabid">Aeq</span><span class="scilaboperator">=</span><span class="scilabopenclose">[</span><span class="scilabopenclose">]</span> +<span class="scilabid">beq</span><span class="scilaboperator">=</span><span class="scilabopenclose">[</span><span class="scilabopenclose">]</span> +<span class="scilabid">lb</span><span class="scilaboperator">=</span><span class="scilabopenclose">[</span><span class="scilaboperator">-</span><span class="scilabconstants">%inf</span><span class="scilabdefault">,</span><span class="scilaboperator">-</span><span class="scilabconstants">%inf</span><span class="scilabdefault">,</span><span class="scilaboperator">-</span><span class="scilabconstants">%inf</span><span class="scilabopenclose">]</span> +<span class="scilabid">ub</span><span class="scilaboperator">=</span><span class="scilabopenclose">[</span><span class="scilabconstants">%inf</span><span class="scilabdefault">,</span><span class="scilabconstants">%inf</span><span class="scilabdefault">,</span><span class="scilabconstants">%inf</span><span class="scilabopenclose">]</span> +<span class="scilabopenclose">[</span><span class="scilabid">xopt</span><span class="scilabdefault">,</span><span class="scilabid">fopt</span><span class="scilabdefault">,</span><span class="scilabid">exitflag</span><span class="scilabdefault">,</span><span class="scilabid">output</span><span class="scilabdefault">,</span><span class="scilabid">lambda</span><span class="scilabopenclose">]</span><span class="scilaboperator">=</span> <span class="scilabid">linprog</span><span class="scilabopenclose">(</span><span class="scilabid">c</span><span class="scilabdefault">,</span><span class="scilabid">A</span><span class="scilabdefault">,</span><span class="scilabid">b</span><span class="scilabdefault">,</span><span class="scilabid">Aeq</span><span class="scilabdefault">,</span><span class="scilabid">beq</span><span class="scilabdefault">,</span><span class="scilabid">lb</span><span class="scilabdefault">,</span><span class="scilabid">ub</span><span class="scilabopenclose">)</span> +<span class="scilabcomment">// Press ENTER to continue</span></pre></td><td valign="top"><a href="scilab://scilab.execexample/"><img src="ScilabExecute.png" border="0"/></a></td><td valign="top"><a href="scilab://scilab.editexample/"><img src="ScilabEdit.png" border="0"/></a></td><td></td></tr></table></div></div> + +<div class="refsection"><h3 class="title">Examples</h3> + <div class="programlisting"><table border="0" width="100%"><tr><td width="98%"><pre class="scilabcode"><span class="scilabid">filepath</span> <span class="scilaboperator">=</span> <a class="scilabcommand" href="scilab://get_absolute_file_path">get_absolute_file_path</a><span class="scilabopenclose">(</span><span class="scilabstring">'</span><span class="scilabstring">linprog.dem.sce</span><span class="scilabstring">'</span><span class="scilabopenclose">)</span><span class="scilabdefault">;</span> +<span class="scilabid">filepath</span> <span class="scilaboperator">=</span> <span class="scilabid">filepath</span> <span class="scilaboperator">+</span> <span class="scilabstring">"</span><span class="scilabstring">exmip1.mps</span><span class="scilabstring">"</span> +<span class="scilabopenclose">[</span><span class="scilabid">xopt</span><span class="scilabdefault">,</span><span class="scilabid">fopt</span><span class="scilabdefault">,</span><span class="scilabid">exitflag</span><span class="scilabdefault">,</span><span class="scilabid">output</span><span class="scilabdefault">,</span><span class="scilabid">lambda</span><span class="scilabopenclose">]</span> <span class="scilaboperator">=</span><span class="scilabid">linprog</span><span class="scilabopenclose">(</span><span class="scilabid">filepath</span><span class="scilabopenclose">)</span><span class="scilabdefault">;</span></pre></td><td valign="top"><a href="scilab://scilab.execexample/"><img src="ScilabExecute.png" border="0"/></a></td><td valign="top"><a href="scilab://scilab.editexample/"><img src="ScilabEdit.png" border="0"/></a></td><td></td></tr></table></div></div> + +<div class="refsection"><h3 class="title">Authors</h3> + <ul class="itemizedlist"><li class="member">Bhanu Priya Sayal, Guru Pradeep Reddy</li></ul></div> + <br /> + + <div class="manualnavbar"> + <table width="100%"> + <tr><td colspan="3" class="next"><a href="http://bugzilla.scilab.org/enter_bug.cgi?product=Scilab%20software&component=Documentation%20pages" class="ulink">Report an issue</a></td></tr> +<tr> + <td width="30%"> + <span class="previous"><a href="fminunc.html"><< fminunc</a></span> + + </td> + <td width="40%" class="center"> + <span class="top"><a href="section_19f4f1e5726c01d683e8b82be0a7e910.html">Symphony Toolbox</a></span> + + </td> + <td width="30%" class="next"> + <span class="next"><a href="lsqlin.html">lsqlin >></a></span> + + </td> + </tr></table> + <hr /> + </div> + </body> +</html> diff --git a/help/en_US/scilab_en_US_help/lsqlin.html b/help/en_US/scilab_en_US_help/lsqlin.html index db24b63..eb1b38d 100644 --- a/help/en_US/scilab_en_US_help/lsqlin.html +++ b/help/en_US/scilab_en_US_help/lsqlin.html @@ -12,7 +12,7 @@ <div class="manualnavbar"> <table width="100%"><tr> <td width="30%"> - <span class="previous"><a href="section_19f4f1e5726c01d683e8b82be0a7e910.html"><< Symphony Toolbox</a></span> + <span class="previous"><a href="linprog.html"><< linprog</a></span> </td> <td width="40%" class="center"> @@ -151,7 +151,7 @@ It has type "struct" and contains the following fields. <tr><td colspan="3" class="next"><a href="http://bugzilla.scilab.org/enter_bug.cgi?product=Scilab%20software&component=Documentation%20pages" class="ulink">Report an issue</a></td></tr> <tr> <td width="30%"> - <span class="previous"><a href="section_19f4f1e5726c01d683e8b82be0a7e910.html"><< Symphony Toolbox</a></span> + <span class="previous"><a href="linprog.html"><< linprog</a></span> </td> <td width="40%" class="center"> diff --git a/help/en_US/scilab_en_US_help/section_19f4f1e5726c01d683e8b82be0a7e910.html b/help/en_US/scilab_en_US_help/section_19f4f1e5726c01d683e8b82be0a7e910.html index a79bad0..a03f091 100644 --- a/help/en_US/scilab_en_US_help/section_19f4f1e5726c01d683e8b82be0a7e910.html +++ b/help/en_US/scilab_en_US_help/section_19f4f1e5726c01d683e8b82be0a7e910.html @@ -31,7 +31,37 @@ <br /><br /> <h3 class="title-part">Symphony Toolbox</h3> -<ul class="list-chapter"><li><a href="lsqlin.html" class="refentry">lsqlin</a> — <span class="refentry-description">Solves a linear quadratic problem.</span></li> +<ul class="list-chapter"><li><a href="fgoalattain.html" class="refentry">fgoalattain</a> — <span class="refentry-description">Solves a multiobjective goal attainment problem</span></li> + + + + + +<li><a href="fminbnd.html" class="refentry">fminbnd</a> — <span class="refentry-description">Solves a multi-variable optimization problem on a bounded interval</span></li> + + + + + +<li><a href="fmincon.html" class="refentry">fmincon</a> — <span class="refentry-description">Solves a multi-variable constrainted optimization problem</span></li> + + + + + +<li><a href="fminunc.html" class="refentry">fminunc</a> — <span class="refentry-description">Solves a multi-variable unconstrainted optimization problem</span></li> + + + + + +<li><a href="linprog.html" class="refentry">linprog</a> — <span class="refentry-description">Solves a linear programming problem.</span></li> + + + + + +<li><a href="lsqlin.html" class="refentry">lsqlin</a> — <span class="refentry-description">Solves a linear quadratic problem.</span></li> |
