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diff --git a/help/en_US/fminunc.xml b/help/en_US/fminunc.xml new file mode 100644 index 0000000..a28a82a --- /dev/null +++ b/help/en_US/fminunc.xml @@ -0,0 +1,196 @@ +<?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) + + ]]></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) + + ]]></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> |