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<?xml version="1.0" encoding="UTF-8"?>
<!--
*
* This help file was generated from fminunc.sci using help_from_sci().
*
-->
<refentry version="5.0-subset Scilab" xml:id="fminunc" xml:lang="en"
xmlns="http://docbook.org/ns/docbook"
xmlns:xlink="http://www.w3.org/1999/xlink"
xmlns:svg="http://www.w3.org/2000/svg"
xmlns:ns3="http://www.w3.org/1999/xhtml"
xmlns:mml="http://www.w3.org/1998/Math/MathML"
xmlns:scilab="http://www.scilab.org"
xmlns:db="http://docbook.org/ns/docbook">
<refnamediv>
<refname>fminunc</refname>
<refpurpose>Solves a multi-variable unconstrainted optimization problem</refpurpose>
</refnamediv>
<refsynopsisdiv>
<title>Calling Sequence</title>
<synopsis>
xopt = fminunc(f,x0)
xopt = fminunc(f,x0,options)
[xopt,fopt] = fminunc(.....)
[xopt,fopt,exitflag]= fminunc(.....)
[xopt,fopt,exitflag,output]= fminunc(.....)
[xopt,fopt,exitflag,output,gradient]=fminunc(.....)
[xopt,fopt,exitflag,output,gradient,hessian]=fminunc(.....)
</synopsis>
</refsynopsisdiv>
<refsection>
<title>Parameters</title>
<variablelist>
<varlistentry><term>f :</term>
<listitem><para> a function, representing the objective function of the problem</para></listitem></varlistentry>
<varlistentry><term>x0 :</term>
<listitem><para> a vector of doubles, containing the starting of variables.</para></listitem></varlistentry>
<varlistentry><term>options:</term>
<listitem><para> a list, containing the option for user to specify. See below for details.</para></listitem></varlistentry>
<varlistentry><term>xopt :</term>
<listitem><para> a vector of doubles, the computed solution of the optimization problem.</para></listitem></varlistentry>
<varlistentry><term>fopt :</term>
<listitem><para> a scalar of double, the function value at x.</para></listitem></varlistentry>
<varlistentry><term>exitflag :</term>
<listitem><para> a scalar of integer, containing the flag which denotes the reason for termination of algorithm. See below for details.</para></listitem></varlistentry>
<varlistentry><term>output :</term>
<listitem><para> a structure, containing the information about the optimization. See below for details.</para></listitem></varlistentry>
<varlistentry><term>gradient :</term>
<listitem><para> a vector of doubles, containing the the gradient of the solution.</para></listitem></varlistentry>
<varlistentry><term>hessian :</term>
<listitem><para> a matrix of doubles, containing the the hessian of the solution.</para></listitem></varlistentry>
</variablelist>
</refsection>
<refsection>
<title>Description</title>
<para>
Search the minimum of an unconstrained optimization problem specified by :
Find the minimum of f(x) such that
</para>
<para>
<latex>
\begin{eqnarray}
&\mbox{min}_{x}
& f(x)\\
\end{eqnarray}
</latex>
</para>
<para>
The routine calls Ipopt for solving the Un-constrained Optimization problem, Ipopt is a library written in C++.
</para>
<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.
<itemizedlist>
<listitem>Syntax : options= list("MaxIter", [---], "CpuTime", [---], "Gradient", ---, "Hessian", ---);</listitem>
<listitem>MaxIter : a Scalar, containing the Maximum Number of Iteration that the solver should take.</listitem>
<listitem>CpuTime : a Scalar, containing the Maximum amount of CPU Time that the solver should take.</listitem>
<listitem>Gradient : a function, representing the gradient function of the Objective in Vector Form.</listitem>
<listitem>Hessian : a function, representing the hessian function of the Objective in Symmetric Matrix Form.</listitem>
<listitem>Default Values : options = list("MaxIter", [3000], "CpuTime", [600]);</listitem>
</itemizedlist>
</para>
<para>
The exitflag allows to know the status of the optimization which is given back by Ipopt.
<itemizedlist>
<listitem>exitflag=0 : Optimal Solution Found </listitem>
<listitem>exitflag=1 : Maximum Number of Iterations Exceeded. Output may not be optimal.</listitem>
<listitem>exitflag=2 : Maximum CPU Time exceeded. Output may not be optimal.</listitem>
<listitem>exitflag=3 : Stop at Tiny Step.</listitem>
<listitem>exitflag=4 : Solved To Acceptable Level.</listitem>
<listitem>exitflag=5 : Converged to a point of local infeasibility.</listitem>
</itemizedlist>
</para>
<para>
For more details on exitflag see the ipopt documentation, go to http://www.coin-or.org/Ipopt/documentation/
</para>
<para>
The output data structure contains detailed informations about the optimization process.
It has type "struct" and contains the following fields.
<itemizedlist>
<listitem>output.Iterations: The number of iterations performed during the search</listitem>
<listitem>output.Cpu_Time: The total cpu-time spend during the search</listitem>
<listitem>output.Objective_Evaluation: The number of Objective Evaluations performed during the search</listitem>
<listitem>output.Dual_Infeasibility: The Dual Infeasiblity of the final soution</listitem>
</itemizedlist>
</para>
<para>
</para>
</refsection>
<refsection>
<title>Examples</title>
<programlisting role="example"><![CDATA[
//Find x in R^2 such that it minimizes the Rosenbrock function
//f = 100*(x2 - x1^2)^2 + (1-x1)^2
//Objective function to be minimised
function y= f(x)
y= 100*(x(2) - x(1)^2)^2 + (1-x(1))^2;
endfunction
//Starting point
x0=[-1,2];
//Gradient of objective function
function y= fGrad(x)
y= [-400*x(1)*x(2) + 400*x(1)^3 + 2*x(1)-2, 200*(x(2)-x(1)^2)];
endfunction
//Hessian of Objective Function
function y= fHess(x)
y= [1200*x(1)^2- 400*x(2) + 2, -400*x(1);-400*x(1), 200 ];
endfunction
//Options
options=list("MaxIter", [1500], "CpuTime", [500], "Gradient", fGrad, "Hessian", fHess);
//Calling Ipopt
[xopt,fopt,exitflag,output,gradient,hessian]=fminunc(f,x0,options)
// Press ENTER to continue
]]></programlisting>
</refsection>
<refsection>
<title>Examples</title>
<programlisting role="example"><![CDATA[
//Find x in R^2 such that the below function is minimum
//f = x1^2 + x2^2
//Objective function to be minimised
function y= f(x)
y= x(1)^2 + x(2)^2;
endfunction
//Starting point
x0=[2,1];
//Calling Ipopt
[xopt,fopt]=fminunc(f,x0)
// Press ENTER to continue
]]></programlisting>
</refsection>
<refsection>
<title>Examples</title>
<programlisting role="example"><![CDATA[
//The below problem is an unbounded problem:
//Find x in R^2 such that the below function is minimum
//f = - x1^2 - x2^2
//Objective function to be minimised
function y= f(x)
y= -x(1)^2 - x(2)^2;
endfunction
//Starting point
x0=[2,1];
//Gradient of objective function
function y= fGrad(x)
y= [-2*x(1),-2*x(2)];
endfunction
//Hessian of Objective Function
function y= fHess(x)
y= [-2,0;0,-2];
endfunction
//Options
options=list("MaxIter", [1500], "CpuTime", [500], "Gradient", fGrad, "Hessian", fHess);
//Calling Ipopt
[xopt,fopt,exitflag,output,gradient,hessian]=fminunc(f,x0,options)
]]></programlisting>
</refsection>
<refsection>
<title>Authors</title>
<simplelist type="vert">
<member>R.Vidyadhar , Vignesh Kannan</member>
</simplelist>
</refsection>
</refentry>
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