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diff --git a/help/en_US/scilab_en_US_help/symphony.html~ b/help/en_US/scilab_en_US_help/symphony.html~ new file mode 100644 index 0000000..0b78b0d --- /dev/null +++ b/help/en_US/scilab_en_US_help/symphony.html~ @@ -0,0 +1,318 @@ +<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="section_ed3c614d9a2555a6802170ca29940f55.html"><< Fmincon Toolbox</a></span> + + </td> + <td width="40%" class="center"> + <span class="top"><a href="section_ed3c614d9a2555a6802170ca29940f55.html">Fmincon Toolbox</a></span> + + </td> + <td width="30%" class="next"> + <span class="next"><a href="optimget.html">optimget >></a></span> + + </td> + </tr></table> + <hr /> + </div> + + + + <span class="path"><a href="index.html">Fmincon Toolbox</a> >> <a href="section_ed3c614d9a2555a6802170ca29940f55.html">Fmincon Toolbox</a> > fmincon</span> + + <br /><br /> + <div class="info"></div> + + <div class="refnamediv"><h1 class="refname">fmincon</h1><p class="refpurpose">Solves a nonlinearily constrained optimization 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">fmincon</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">x</span><span class="default"> = </span><span class="functionid">fmincon</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">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">fmincon</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">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">fmincon</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">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">fmincon</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">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">fmincon</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">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="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">grad</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">fun:</span> + <dd><p class="para">a function, the function to minimize. See below for the complete specifications.</p></dd></dt> + <dt><span class="term">x0:</span> + <dd><p class="para">a nx1 or 1xn matrix of doubles, where n is the number of variables. The initial guess for the optimization algorithm.</p></dd></dt> + <dt><span class="term">A:</span> + <dd><p class="para">a nil x n matrix of doubles, where n is the number of variables and nil is the number of linear inequalities. If A==[] and b==[], it is assumed that there is no linear inequality constraints. If (A==[] & b<>[]), fmincon generates an error (the same happens if (A<>[] & b==[])).</p></dd></dt> + <dt><span class="term">b:</span> + <dd><p class="para">a nil x 1 matrix of doubles, where nil is the number of linear inequalities.</p></dd></dt> + <dt><span class="term">Aeq:</span> + <dd><p class="para">a nel x n matrix of doubles, where n is the number of variables and nel is the number of linear equalities. If A==[] and b==[], it is assumed that there is no linear equality constraints. If (Aeq==[] & beq<>[]), fmincon generates an error (the same happens if (Aeq<>[] & beq==[])).</p></dd></dt> + <dt><span class="term">beq:</span> + <dd><p class="para">a nel x 1 matrix of doubles, where nel is the number of linear inequalities.</p></dd></dt> + <dt><span class="term">lb:</span> + <dd><p class="para">a nx1 or 1xn matrix of doubles, where n is the number of variables. The lower bound for x. If lb==[], then the lower bound is automatically set to -inf.</p></dd></dt> + <dt><span class="term">ub:</span> + <dd><p class="para">a nx1 or 1xn matrix of doubles, where n is the number of variables. The upper bound for x. If lb==[], then the upper bound is automatically set to +inf.</p></dd></dt> + <dt><span class="term">nonlcon:</span> + <dd><p class="para">a function, the nonlinear constraints. See below for the complete specifications.</p></dd></dt> + <dt><span class="term">x:</span> + <dd><p class="para">a nx1 matrix of doubles, the computed solution of the optimization problem</p></dd></dt> + <dt><span class="term">fval:</span> + <dd><p class="para">a 1x1 matrix of doubles, the function value at x</p></dd></dt> + <dt><span class="term">exitflag:</span> + <dd><p class="para">a 1x1 matrix of floating point integers, the exit status. See below for details.</p></dd></dt> + <dt><span class="term">output:</span> + <dd><p class="para">a struct, the details of the optimization process. See below for details.</p></dd></dt> + <dt><span class="term">lambda:</span> + <dd><p class="para">a struct, the Lagrange multipliers at optimum. See below for details.</p></dd></dt> + <dt><span class="term">grad:</span> + <dd><p class="para">a nx1 matrix of doubles, the gradient of the objective function at optimum</p></dd></dt> + <dt><span class="term">hessian:</span> + <dd><p class="para">a nxn matrix of doubles, the Hessian of the objective function at optimum</p></dd></dt> + <dt><span class="term">options:</span> + <dd><p class="para">an optional struct, as provided by optimset</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">c(x)<=0, ceq(x)<=0, A*x<=b, Aeq*x=beq and lb<=x<=ub.</p> + <p class="para"><span><img src='./_LaTeX_fmincon.xml_1.png' style='position:relative;top:64px;width:186px;height:136px'/></span></p> + <p class="para">Currently, we use ipopt for the actual solver of fmincon.</p> + <p class="para">See the demonstrations for additionnal examples.</p> + <p class="para">The objective function must have header : +<div class="programlisting"><table border="0" width="100%"><tr><td width="98%"><pre class="scilabcode"><span class="scilabid">f</span> <span class="scilaboperator">=</span> <span class="scilabid">objfun</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 doubles and f is a 1 x 1 matrix of doubles. +On input, the variable x contains the current point and, on output, +the variable f must contain the objective function value.</p> + <p class="para">By default, fmincon uses finite differences with order 2 formulas and +optimum step size in order to compute a numerical gradient of the +objective function. +If we can provide exact gradients, we should do so since it improves +the convergence speed of the optimization algorithm. +In order to use exact gradients, we must update the header of the +objective function to : +<div class="programlisting"><table border="0" width="100%"><tr><td width="98%"><pre class="scilabcode"><span class="scilabopenclose">[</span><span class="scilabid">f</span><span class="scilabdefault">,</span><span class="scilabid">G</span><span class="scilabopenclose">]</span> <span class="scilaboperator">=</span> <span class="scilabid">objfungrad</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 doubles, f is a 1 x 1 matrix of doubles +and G is a n x 1 matrix of doubles. +On input, the variable x contains the current point and, on output, +the variable f must contain the objective function value and the variable +G must contain the gradient of the objective function. +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">options</span> <span class="scilaboperator">=</span> <a class="scilabmacro" href="optimset.html">optimset</a><span class="scilabopenclose">(</span><span class="scilabstring">"</span><span class="scilabstring">GradObj</span><span class="scilabstring">"</span><span class="scilabdefault">,</span><span class="scilabstring">"</span><span class="scilabstring">on</span><span class="scilabstring">"</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 fmincon 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 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 doubles, c is a nni x 1 matrix of doubles and +ceq is a nne x 1 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, fmincon uses finite differences with order 2 formulas and +optimum step size in order to compute a numerical gradient of the +constraint function. +In order to use exact gradients, we must update the header of the +constraint function to : +<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="scilabdefault">,</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 x is a n x 1 matrix of doubles, c is a nni x 1 matrix of doubles, +ceq is a nne x 1 matrix of doubles, DC is a n x nni matrix of doubles and +DCeq is a n x nne matrix of doubles. +On input, the variable x contains the current point and, on output, +the variable c must contain the nonlinear inequality constraint function value, +the variable ceq must contain the nonlinear equality constraint function value, +the variable DC must contain the Jacobian matrix of the nonlinear inequality constraints +and the variable DCeq must contain the Jacobian matrix of the nonlinear equality constraints. +The i-th nonlinear inequality constraint is associated to the i-th column of +the matrix DC, i.e, it is stored in DC(:,i) (same for DCeq). +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">options</span> <span class="scilaboperator">=</span> <a class="scilabmacro" href="optimset.html">optimset</a><span class="scilabopenclose">(</span><span class="scilabstring">"</span><span class="scilabstring">GradConstr</span><span class="scilabstring">"</span><span class="scilabdefault">,</span><span class="scilabstring">"</span><span class="scilabstring">on</span><span class="scilabstring">"</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></p> + <p class="para">By default, fmincon uses a L-BFGS formula to compute an +approximation of the Hessian of the Lagrangian. +Notice that this is different from Matlab's fmincon, which +default is to use a BFGS.</p> + <p class="para">The exitflag variable allows to know the status of the optimization. +<ul class="itemizedlist"><li>exitflag=0 : Number of iterations exceeded options.MaxIter or number of function evaluations exceeded options.FunEvals.</li> +<li>exitflag=1 : First-order optimality measure was less than options.TolFun, and maximum constraint violation was less than options.TolCon.</li> +<li>exitflag=-1 : The output function terminated the algorithm.</li> +<li>exitflag=-2 : No feasible point was found.</li> +<li>exitflag=%nan : Other type of termination.</li></ul></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.funcCount: the number of function evaluations during the search</li> +<li>output.stepsize: an empty matrix</li> +<li>output.algorithm : the string containing the name of the algorithm. In the current version, algorithm="ipopt".</li> +<li>output.firstorderopt: the max-norm of the first-order KKT conditions.</li> +<li>output.constrviolation: the max-norm of the constraint violation.</li> +<li>output.cgiterations: the number of preconditionned conjugate gradient steps. In the current version, cgiterations=0.</li> +<li>output.message: a string containing a message describing the status of the optimization.</li></ul></p> + <p class="para">The lambda data structure contains the Lagrange multipliers at the +end of optimization. +It has type "struct" and contains the following +fields. +<ul class="itemizedlist"><li>lambda.lower: the Lagrange multipliers for the lower bound constraints. In the current version, an empty matrix.</li> +<li>lambda.upper: the Lagrange multipliers for the upper bound constraints. In the current version, an empty matrix.</li> +<li>lambda.eqlin: the Lagrange multipliers for the linear equality constraints.</li> +<li>lambda.eqnonlin: the Lagrange multipliers for the nonlinear equality constraints.</li> +<li>lambda.ineqlin: the Lagrange multipliers for the linear inequality constraints.</li> +<li>lambda.ineqnonlin: the Lagrange multipliers for the nonlinear inequality constraints.</li></ul></p> + <p class="para">TODO : exitflag=2 : Change in x was less than options.TolX and maximum constraint violation was less than options.TolCon. +TODO : exitflag=-3 : Current point x went below options.ObjectiveLimit and maximum constraint violation was less than options.TolCon. +TODO : fill lambda.lower and lambda.upper consistently. See ticket #111 : http://forge.scilab.org/index.php/p/sci-ipopt/issues/111/ +TODO : test with A, b +TODO : test with Aeq, beq +TODO : test with ceq +TODO : avoid using global for ipopt_data +TODO : implement Display option +TODO : implement FinDiffType option +TODO : implement MaxFunEvals option +TODO : implement DerivativeCheck option +TODO : implement MaxIter option +TODO : implement OutputFcn option +TODO : implement PlotFcns option +TODO : implement TolFun option +TODO : implement TolCon option +TODO : implement TolX option +TODO : implement Hessian option +TODO : check that the hessian output argument is Hessian of f only +TODO : test all exitflag values</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">// A basic case :</span> +<span class="scilabcomment">// we provide only the objective function and the nonlinear constraint</span> +<span class="scilabcomment">// function : we let fmincon compute the gradients by numerical</span> +<span class="scilabcomment">// derivatives.</span> +<span class="scilabfkeyword">function</span> <span class="scilabinputoutputargs">f</span><span class="scilaboperator">=</span><span class="scilabfunctionid">objfun</span><span class="scilabopenclose">(</span><span class="scilabinputoutputargs">x</span><span class="scilabopenclose">)</span> +<span class="scilabinputoutputargs">f</span> <span class="scilaboperator">=</span> <a class="scilabcommand" href="scilab://exp">exp</a><span class="scilabopenclose">(</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="scilabopenclose">(</span><span class="scilabnumber">4</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">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">4</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">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">1</span><span class="scilabopenclose">)</span> +<span class="scilabfkeyword">endfunction</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">confun</span><span class="scilabopenclose">(</span><span class="scilabinputoutputargs">x</span><span class="scilabopenclose">)</span> +<span class="scilabcomment">// Nonlinear inequality constraints</span> +<span class="scilabinputoutputargs">c</span> <span class="scilaboperator">=</span> <span class="scilabopenclose">[</span> +<span class="scilabnumber">1.5</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">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">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">10</span> +<span class="scilabopenclose">]</span> +<span class="scilabcomment">// Nonlinear equality constraints</span> +<span class="scilabinputoutputargs">ceq</span> <span class="scilaboperator">=</span> <span class="scilabopenclose">[</span><span class="scilabopenclose">]</span> +<span class="scilabfkeyword">endfunction</span> +<span class="scilabcomment">// The initial guess</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="scilabcomment">// The expected solution : only 4 digits are guaranteed</span> +<span class="scilabid">xopt</span> <span class="scilaboperator">=</span> <span class="scilabopenclose">[</span><span class="scilaboperator">-</span><span class="scilabnumber">9.547345885974547</span> <span class="scilabnumber">1.047408305349257</span><span class="scilabopenclose">]</span> +<span class="scilabid">fopt</span> <span class="scilaboperator">=</span> <span class="scilabnumber">0.023551460139148</span> +<span class="scilabcomment">// Run fmincon</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="scilabspecial">..</span> +<span class="scilabid">fmincon</span> <span class="scilabopenclose">(</span> <span class="scilabfunctionid">objfun</span><span class="scilabdefault">,</span><span class="scilabid">x0</span><span class="scilabdefault">,</span><span class="scilabopenclose">[</span><span class="scilabopenclose">]</span><span class="scilabdefault">,</span><span class="scilabopenclose">[</span><span class="scilabopenclose">]</span><span class="scilabdefault">,</span><span class="scilabopenclose">[</span><span class="scilabopenclose">]</span><span class="scilabdefault">,</span><span class="scilabopenclose">[</span><span class="scilabopenclose">]</span><span class="scilabdefault">,</span><span class="scilabopenclose">[</span><span class="scilabopenclose">]</span><span class="scilabdefault">,</span><span class="scilabopenclose">[</span><span class="scilabopenclose">]</span><span class="scilabdefault">,</span> <span class="scilabfunctionid">confun</span> <span class="scilabstring">)</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">// A case where we provide the gradient of the objective</span> +<span class="scilabcomment">// function and the Jacobian matrix of the constraints.</span> +<span class="scilabcomment">// The objective function and its gradient</span> +<span class="scilabfkeyword">function</span> <span class="scilabopenclose">[</span><span class="scilabinputoutputargs">f</span><span class="scilabdefault">, </span><span class="scilabinputoutputargs">G</span><span class="scilabopenclose">]</span><span class="scilaboperator">=</span><span class="scilabfunctionid">objfungrad</span><span class="scilabopenclose">(</span><span class="scilabinputoutputargs">x</span><span class="scilabopenclose">)</span> +<span class="scilabopenclose">[</span><span class="scilabid">lhs</span><span class="scilabdefault">,</span><span class="scilabid">rhs</span><span class="scilabopenclose">]</span><span class="scilaboperator">=</span><a class="scilabcommand" href="scilab://argn">argn</a><span class="scilabopenclose">(</span><span class="scilabopenclose">)</span> +<span class="scilabinputoutputargs">f</span> <span class="scilaboperator">=</span> <a class="scilabcommand" href="scilab://exp">exp</a><span class="scilabopenclose">(</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="scilabopenclose">(</span><span class="scilabnumber">4</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">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">4</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">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">1</span><span class="scilabopenclose">)</span> +<span class="scilabskeyword">if</span> <span class="scilabopenclose">(</span> <span class="scilabid">lhs</span> <span class="scilaboperator">></span> <span class="scilabnumber">1</span> <span class="scilabopenclose">)</span> <span class="scilabskeyword">then</span> +<span class="scilabinputoutputargs">G</span> <span class="scilaboperator">=</span> <span class="scilabopenclose">[</span> +<span class="scilabinputoutputargs">f</span> <span class="scilaboperator">+</span> <a class="scilabcommand" href="scilab://exp">exp</a><span class="scilabopenclose">(</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="scilabopenclose">(</span><span class="scilabnumber">8</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">4</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> +<a class="scilabcommand" href="scilab://exp">exp</a><span class="scilabopenclose">(</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="scilabopenclose">(</span><span class="scilabnumber">4</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">4</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="scilabopenclose">)</span> +<span class="scilabopenclose">]</span> +<span class="scilabskeyword">end</span> +<span class="scilabfkeyword">endfunction</span> +<span class="scilabcomment">// The nonlinear constraints and the Jacobian</span> +<span class="scilabcomment">// matrix of the 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="scilabdefault">, </span><span class="scilabinputoutputargs">DC</span><span class="scilabdefault">, </span><span class="scilabinputoutputargs">DCeq</span><span class="scilabopenclose">]</span><span class="scilaboperator">=</span><span class="scilabfunctionid">confungrad</span><span class="scilabopenclose">(</span><span class="scilabinputoutputargs">x</span><span class="scilabopenclose">)</span> +<span class="scilabcomment">// Inequality constraints</span> +<span class="scilabinputoutputargs">c</span><span class="scilabopenclose">(</span><span class="scilabnumber">1</span><span class="scilabopenclose">)</span> <span class="scilaboperator">=</span> <span class="scilabnumber">1.5</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">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">c</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">2</span><span class="scilabopenclose">)</span><span class="scilaboperator">-</span><span class="scilabnumber">10</span> +<span class="scilabcomment">// No nonlinear equality constraints</span> +<span class="scilabinputoutputargs">ceq</span><span class="scilaboperator">=</span><span class="scilabopenclose">[</span><span class="scilabopenclose">]</span> +<span class="scilabopenclose">[</span><span class="scilabid">lhs</span><span class="scilabdefault">,</span><span class="scilabid">rhs</span><span class="scilabopenclose">]</span><span class="scilaboperator">=</span><a class="scilabcommand" href="scilab://argn">argn</a><span class="scilabopenclose">(</span><span class="scilabopenclose">)</span> +<span class="scilabskeyword">if</span> <span class="scilabopenclose">(</span> <span class="scilabid">lhs</span> <span class="scilaboperator">></span> <span class="scilabnumber">2</span> <span class="scilabopenclose">)</span> <span class="scilabskeyword">then</span> +<span class="scilabcomment">// DC(:,i) = gradient of the i-th constraint</span> +<span class="scilabcomment">// DC = [</span> +<span class="scilabcomment">// Dc1/Dx1 Dc2/Dx1</span> +<span class="scilabcomment">// Dc1/Dx2 Dc2/Dx2</span> +<span class="scilabcomment">// ]</span> +<span class="scilabinputoutputargs">DC</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="scilabdefault">,</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">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="scilabdefault">,</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="scilabinputoutputargs">DCeq</span> <span class="scilaboperator">=</span> <span class="scilabopenclose">[</span><span class="scilabopenclose">]</span> +<span class="scilabskeyword">end</span> +<span class="scilabfkeyword">endfunction</span> +<span class="scilabcomment">// Test with both gradient of objective and gradient of constraints</span> +<span class="scilabid">options</span> <span class="scilaboperator">=</span> <a class="scilabmacro" href="optimset.html">optimset</a><span class="scilabopenclose">(</span><span class="scilabstring">"</span><span class="scilabstring">GradObj</span><span class="scilabstring">"</span><span class="scilabdefault">,</span><span class="scilabstring">"</span><span class="scilabstring">on</span><span class="scilabstring">"</span><span class="scilabdefault">,</span><span class="scilabstring">"</span><span class="scilabstring">GradConstr</span><span class="scilabstring">"</span><span class="scilabdefault">,</span><span class="scilabstring">"</span><span class="scilabstring">on</span><span class="scilabstring">"</span><span class="scilabopenclose">)</span><span class="scilabdefault">;</span> +<span class="scilabcomment">// The initial guess</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="scilabcomment">// The expected solution : only 4 digits are guaranteed</span> +<span class="scilabid">xopt</span> <span class="scilaboperator">=</span> <span class="scilabopenclose">[</span><span class="scilaboperator">-</span><span class="scilabnumber">9.547345885974547</span> <span class="scilabnumber">1.047408305349257</span><span class="scilabopenclose">]</span> +<span class="scilabid">fopt</span> <span class="scilaboperator">=</span> <span class="scilabnumber">0.023551460139148</span> +<span class="scilabcomment">// Run fmincon</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="scilabspecial">..</span> +<span class="scilabid">fmincon</span><span class="scilabopenclose">(</span><span class="scilabfunctionid">objfungrad</span><span class="scilabdefault">,</span><span class="scilabid">x0</span><span class="scilabdefault">,</span><span class="scilabopenclose">[</span><span class="scilabopenclose">]</span><span class="scilabdefault">,</span><span class="scilabopenclose">[</span><span class="scilabopenclose">]</span><span class="scilabdefault">,</span><span class="scilabopenclose">[</span><span class="scilabopenclose">]</span><span class="scilabdefault">,</span><span class="scilabopenclose">[</span><span class="scilabopenclose">]</span><span class="scilabdefault">,</span><span class="scilabopenclose">[</span><span class="scilabopenclose">]</span><span class="scilabdefault">,</span><span class="scilabopenclose">[</span><span class="scilabopenclose">]</span><span class="scilabdefault">,</span> <span class="scilabfunctionid">confungrad</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">// A case where we set the bounds of the optimization.</span> +<span class="scilabcomment">// By default, the bounds are set to infinity.</span> +<span class="scilabfkeyword">function</span> <span class="scilabinputoutputargs">f</span><span class="scilaboperator">=</span><span class="scilabfunctionid">objfun</span><span class="scilabopenclose">(</span><span class="scilabinputoutputargs">x</span><span class="scilabopenclose">)</span> +<span class="scilabinputoutputargs">f</span> <span class="scilaboperator">=</span> <a class="scilabcommand" href="scilab://exp">exp</a><span class="scilabopenclose">(</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="scilabopenclose">(</span><span class="scilabnumber">4</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">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">4</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">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">1</span><span class="scilabopenclose">)</span> +<span class="scilabfkeyword">endfunction</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">confun</span><span class="scilabopenclose">(</span><span class="scilabinputoutputargs">x</span><span class="scilabopenclose">)</span> +<span class="scilabcomment">// Nonlinear inequality constraints</span> +<span class="scilabinputoutputargs">c</span> <span class="scilaboperator">=</span> <span class="scilabopenclose">[</span> +<span class="scilabnumber">1.5</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">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">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">10</span> +<span class="scilabopenclose">]</span> +<span class="scilabcomment">// Nonlinear equality constraints</span> +<span class="scilabinputoutputargs">ceq</span> <span class="scilaboperator">=</span> <span class="scilabopenclose">[</span><span class="scilabopenclose">]</span> +<span class="scilabfkeyword">endfunction</span> +<span class="scilabcomment">// The initial guess</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="scilabcomment">// The expected solution</span> +<span class="scilabid">xopt</span> <span class="scilaboperator">=</span> <span class="scilabopenclose">[</span><span class="scilabnumber">0</span> <span class="scilabnumber">1.5</span><span class="scilabopenclose">]</span> +<span class="scilabid">fopt</span> <span class="scilaboperator">=</span> <span class="scilabnumber">8.5</span> +<span class="scilabcomment">// Make sure that x(1)</span><span class="scilabcomment">></span><span class="scilabcomment">=0, and x(2)</span><span class="scilabcomment">></span><span class="scilabcomment">=0</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="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">// Run fmincon</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">fmincon</span> <span class="scilabopenclose">(</span> <span class="scilabfunctionid">objfun</span> <span class="scilabdefault">,</span> <span class="scilabid">x0</span><span class="scilabdefault">,</span><span class="scilabopenclose">[</span><span class="scilabopenclose">]</span><span class="scilabdefault">,</span><span class="scilabopenclose">[</span><span class="scilabopenclose">]</span><span class="scilabdefault">,</span><span class="scilabopenclose">[</span><span class="scilabopenclose">]</span><span class="scilabdefault">,</span><span class="scilabopenclose">[</span><span class="scilabopenclose">]</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">confun</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">Michael Baudin, DIGITEO, 2010</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_ed3c614d9a2555a6802170ca29940f55.html"><< Fmincon Toolbox</a></span> + + </td> + <td width="40%" class="center"> + <span class="top"><a href="section_ed3c614d9a2555a6802170ca29940f55.html">Fmincon Toolbox</a></span> + + </td> + <td width="30%" class="next"> + <span class="next"><a href="optimget.html">optimget >></a></span> + + </td> + </tr></table> + <hr /> + </div> + </body> +</html> |