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    <span class="path"><a href="index.html">FOSSEE Optimization Toolbox</a> &gt;&gt; <a href="section_44e1f57c5225357b5fe53cb5fad967e9.html">FOSSEE Optimization Toolbox</a> &gt; 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">Input 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 &#0039;n&#0039; is the number of Variables.</p></dd></dt>
   <dt><span class="term">intcon :</span>
      <dd><p class="para">A vector of integers, representing the variables that 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></dl></div>
<div class="refsection"><h3 class="title">Outputs</h3>
 <dl><dt><span class="term">xopt :</span>
      <dd><p class="para">A vector of doubles, containing the computed solution of the optimization problem.</p></dd></dt>
   <dt><span class="term">fopt :</span>
      <dd><p class="para">A double, containing the the function value at x.</p></dd></dt>
   <dt><span class="term">exitflag :</span>
      <dd><p class="para">An 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&#0039;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&#0039;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">intfminunc calls Bonmin, which is an optimization library written in C++, to solve the bound optimization problem.</p>
  <p class="para"><h3 class="title">Options</h3>
The options allow the user to set various parameters of the Optimization problem. The syntax for the options is given by:</p>
   <p class="para">options= list(&#0034;IntegerTolerance&#0034;, [---], &#0034;MaxNodes&#0034;,[---], &#0034;MaxIter&#0034;, [---], &#0034;AllowableGap&#0034;,[---] &#0034;CpuTime&#0034;, [---],&#0034;gradobj&#0034;, &#0034;off&#0034;, &#0034;hessian&#0034;, &#0034;off&#0034; );
<ul class="itemizedlist"><li>IntegerTolerance : A Scalar, a number with that value of an integer is considered integer.</li>
<li>MaxNodes : A Scalar, containing the maximum number of nodes that the solver should search.</li>
<li>CpuTime : A scalar, specifying the maximum amount of CPU Time in seconds that the solver should take.</li>
<li>AllowableGap : A scalar, that specifies the gap between the computed solution and the the objective value of the best known solution stop, at which the tree search can be stopped.</li>
<li>MaxIter : A scalar, specifying the maximum number of iterations 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></ul>
   The default values for the various items are given as:</p>
   <p class="para">options = list(&#0039;integertolerance&#0039;,1d-06,&#0039;maxnodes&#0039;,2147483647,&#0039;cputime&#0039;,1d10,&#0039;allowablegap&#0039;,0,&#0039;maxiter&#0039;,2147483647,&#0039;gradobj&#0039;,&#0034;off&#0034;,&#0039;hessian&#0039;,&#0034;off&#0034;)</p>
     <p class="para"></p>
   <p class="para">The exitflag allows to know the status of the optimization which is given back by Ipopt.
<ul class="itemizedlist"><li>0 : Optimal Solution Found</li>
<li>1 : InFeasible Solution.</li>
<li>2 : Objective Function is Continuous Unbounded.</li>
<li>3 : Limit Exceeded.</li>
<li>4 : User Interrupt.</li>
<li>5 : MINLP Error.</li></ul></p>
   <p class="para">For more details on exitflag, see the Bonmin documentation which can be found on http://www.coin-or.org/Bonmin</p>
   <p class="para"></p></div>
<p class="para">A few examples displaying the various functionalities of intfminunc have been provided below. You will find a series of problems and the appropriate code snippets to solve them.</p>

<div class="refsection"><h3 class="title">Example</h3>
<p class="para">We begin with the minimization of a simple non-linear function.</p>
   <p class="para">Find x in R^2 such that it minimizes:</p>
   <p class="para"><span><img src='./_LaTeX_intfminunc.xml_2.png' style='position:relative;top:12px;width:213px;height:83px'/></span></p>
   <p class="para"></p>
   <div class="programlisting"><table border="0" width="100%"><tr><td width="98%"><pre class="scilabcode"><span class="scilabcomment">//Example 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="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">Example</h3>
   <p class="para">We now look at the Rosenbrock function, a non-convex performance test problem for optimization routines. We use this example to illustrate how we can enhance the functionality of intfminunc by setting input options. We can pre-define the gradient of the objective function and/or the hessian of the lagrange function and thereby improve the speed of computation. This is elaborated on in example 2. We also set solver parameters using the options.</p>
 <p class="para"><span><img src='./_LaTeX_intfminunc.xml_3.png' style='position:relative;top:12px;width:287px;height:83px'/></span></p>
   <p class="para"></p>
   <div class="programlisting"><table border="0" width="100%"><tr><td width="98%"><pre class="scilabcode"><span class="scilabcomment">///Example 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">&#0034;</span><span class="scilabstring">MaxIter</span><span class="scilabstring">&#0034;</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">&#0034;</span><span class="scilabstring">CpuTime</span><span class="scilabstring">&#0034;</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">Example</h3>
   <p class="para">Unbounded Problems: Find x in R^2 such that it minimizes:</p>
   <p class="para"><span><img src='./_LaTeX_intfminunc.xml_4.png' style='position:relative;top:12px;width:213px;height:83px'/></span></p>
   <p class="para"></p>
   <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">&#0034;</span><span class="scilabstring">gradobj</span><span class="scilabstring">&#0034;</span><span class="scilabdefault">,</span><span class="scilabstring">&#0034;</span><span class="scilabstring">ON</span><span class="scilabstring">&#0034;</span><span class="scilabdefault">,</span><span class="scilabstring">&#0034;</span><span class="scilabstring">hessian</span><span class="scilabstring">&#0034;</span><span class="scilabdefault">,</span><span class="scilabstring">&#0034;</span><span class="scilabstring">on</span><span class="scilabstring">&#0034;</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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