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<span class="path"><a href="index.html">FOSSEE Optimization Toolbox</a> >> <a href="section_2f30ec7805b02b8760d8add3187208be.html">FOSSEE Optimization Toolbox</a> > intfminunc</span>
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<div class="refnamediv"><h1 class="refname">intfminunc</h1>
<p class="refpurpose">Solves an unconstrainted multi-variable mixed integer non linear programming 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">intfminunc</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">intfminunc</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">intcon</span><span class="default">)</span>
<span class="default">xopt</span><span class="default"> = </span><span class="functionid">intfminunc</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">intcon</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">intfminunc</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">intfminunc</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">gradient</span><span class="default">,</span><span class="default">hessian</span><span class="default">]= </span><span class="functionid">intfminunc</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">intcon :</span>
<dd><p class="para">a vector of integers, represents which variables are constrained to be integers</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">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 Objective'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 multi-variable mixed integer non linear programming unconstrained optimization problem specified by :
Find the minimum of f(x) such that</p>
<p class="para"><span><img src='./_LaTeX_intfminunc.xml_1.png' style='position:relative;top:9px;width:213px;height:26px'/></span></p>
<p class="para">The routine calls Bonmin for solving the Un-constrained Optimization problem, Bonmin 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("IntegerTolerance", [---], "MaxNodes", [---], "CpuTime", [---], "AllowableGap", [---], "MaxIter", [---]);</li>
<li>IntegerTolerance : a Scalar, containing the Integer tolerance value that the solver should take.</li>
<li>MaxNodes : a Scalar, containing the maximum nodes that the solver should make.</li>
<li>MaxIter : a Scalar, containing the Maximum Number of Iteration that the solver should take.</li>
<li>AllowableGap : a Scalar, containing the allowable gap value 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 string, to turn on or off the user supplied objective gradient.</li>
<li>hessian : a Scalar, to turn on or off the user supplied objective hessian.</li>
<li>Default Values : options = list('integertolerance',1d-06,'maxnodes',2147483647,'cputime',1d10,'allowablegap',0,'maxiter',2147483647,'gradobj',"off",'hessian',"off")</li></ul></p>
<p class="para">The exitflag allows to know the status of the optimization which is given back by Bonmin.
<ul class="itemizedlist"><li>exitflag=0 : Optimal Solution Found.</li>
<li>exitflag=1 : InFeasible Solution.</li>
<li>exitflag=2 : Output is Continuous Unbounded.</li>
<li>exitflag=3 : Limit Exceeded.</li>
<li>exitflag=4 : User Interrupt.</li>
<li>exitflag=5 : MINLP Error.</li></ul></p>
<p class="para">For more details on exitflag see the Bonmin page, go to http://www.coin-or.org/Bonmin</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="scilabid">intcon</span> <span class="scilaboperator">=</span> <span class="scilabopenclose">[</span><span class="scilabnumber">2</span><span class="scilabopenclose">]</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</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">gradient</span><span class="scilabdefault">,</span><span class="scilabid">hessian</span><span class="scilabopenclose">]</span><span class="scilaboperator">=</span><span class="scilabid">intfminunc</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">intcon</span><span class="scilabdefault">,</span><span class="scilabid">options</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">//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="scilabid">intcon</span> <span class="scilaboperator">=</span> <span class="scilabopenclose">[</span><span class="scilabnumber">1</span><span class="scilabopenclose">]</span><span class="scilabdefault">;</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">intfminunc</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">intcon</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">//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="scilabopenclose">[</span><span class="scilabinputoutputargs">y</span><span class="scilabdefault">, </span><span class="scilabinputoutputargs">g</span><span class="scilabdefault">, </span><span class="scilabinputoutputargs">h</span><span class="scilabopenclose">]</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="scilabinputoutputargs">g</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="scilabinputoutputargs">h</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">//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="scilabid">intcon</span> <span class="scilaboperator">=</span> <span class="scilabopenclose">[</span><span class="scilabnumber">1</span><span class="scilabopenclose">]</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="scilabstring">"</span><span class="scilabstring">ON</span><span class="scilabstring">"</span><span class="scilabdefault">,</span><span class="scilabstring">"</span><span class="scilabstring">hessian</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="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">gradient</span><span class="scilabdefault">,</span><span class="scilabid">hessian</span><span class="scilabopenclose">]</span><span class="scilaboperator">=</span><span class="scilabid">intfminunc</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">intcon</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>
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