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diff --git a/help/en_US/fminbnd.xml b/help/en_US/fminbnd.xml new file mode 100644 index 0000000..baf2f34 --- /dev/null +++ b/help/en_US/fminbnd.xml @@ -0,0 +1,197 @@ +<?xml version="1.0" encoding="UTF-8"?> + +<!-- + * + * This help file was generated from fminbnd.sci using help_from_sci(). + * + --> + +<refentry version="5.0-subset Scilab" xml:id="fminbnd" 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>fminbnd</refname> + <refpurpose>Solves a multi-variable optimization problem on a bounded interval</refpurpose> + </refnamediv> + + +<refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis> + xopt = fminbnd(f,x1,x2) + xopt = fminbnd(f,x1,x2,options) + [xopt,fopt] = fminbnd(.....) + [xopt,fopt,exitflag]= fminbnd(.....) + [xopt,fopt,exitflag,output]=fminbnd(.....) + [xopt,fopt,exitflag,output,lambda]=fminbnd(.....) + + </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>x1 :</term> + <listitem><para> a vector, containing the lower bound of the variables of size (1 X n) or (n X 1) where 'n' is the number of Variables, where n is number of Variables</para></listitem></varlistentry> + <varlistentry><term>x2 :</term> + <listitem><para> a vector, containing the upper bound of the variables of size (1 X n) or (n X 1) or (0 X 0) where 'n' is the number of Variables. If x2 is empty it means upper bound is +infinity</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, containing the the computed solution of the optimization problem.</para></listitem></varlistentry> + <varlistentry><term>fopt :</term> + <listitem><para> a scalar of double, containing the 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>lambda :</term> + <listitem><para> a structure, containing the Lagrange multipliers of lower bound and upper bound at the optimized point. See below for details.</para></listitem></varlistentry> + </variablelist> +</refsection> + +<refsection> + <title>Description</title> + <para> +Search the minimum of a multi-variable function on bounded interval specified by : +Find the minimum of f(x) such that + </para> + <para> +<latex> +\begin{eqnarray} +&\mbox{min}_{x} +& f(x)\\ +& \text{subject to} & x1 \ < x \ < x2 \\ +\end{eqnarray} +</latex> + </para> + <para> +The routine calls Ipopt for solving the Bounded 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", [---], TolX, [----]);</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>TolX : a Scalar, containing the Tolerance value that the solver should take.</listitem> +<listitem>Default Values : options = list("MaxIter", [3000], "CpuTime", [600], TolX, [1e-4]);</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> +The lambda data structure contains the Lagrange multipliers at the end +of optimization. In the current version the values are returned only when the the solution is optimal. +It has type "struct" and contains the following fields. +<itemizedlist> +<listitem>lambda.lower: The Lagrange multipliers for the lower bound constraints.</listitem> +<listitem>lambda.upper: The Lagrange multipliers for the upper bound constraints.</listitem> +</itemizedlist> + </para> + <para> +</para> +</refsection> + +<refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +//Find x in R^6 such that it minimizes: +//f(x)= sin(x1) + sin(x2) + sin(x3) + sin(x4) + sin(x5) + sin(x6) +//-2 <= x1,x2,x3,x4,x5,x6 <= 2 +//Objective function to be minimised +function y=f(x) +y=0 +for i =1:6 +y=y+sin(x(i)); +end +endfunction +//Variable bounds +x1 = [-2, -2, -2, -2, -2, -2]; +x2 = [2, 2, 2, 2, 2, 2]; +//Options +options=list("MaxIter",[1500],"CpuTime", [100],"TolX",[1e-6]) +//Calling Ipopt +[x,fval] =fminbnd(f, x1, x2, options) + + ]]></programlisting> +</refsection> + +<refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +//Find x in R such that it minimizes: +//f(x)= 1/x^2 +//0 <= x <= 1000 +//Objective function to be minimised +function y=f(x) +y=1/x^2 +endfunction +//Variable bounds +x1 = [0]; +x2 = [1000]; +//Calling Ipopt +[x,fval,exitflag,output,lambda] =fminbnd(f, x1, x2) + + ]]></programlisting> +</refsection> + +<refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +//The below problem is an unbounded problem: +//Find x in R^2 such that it minimizes: +//f(x)= -[(x1-1)^2 + (x2-1)^2] +//-inf <= x1,x2 <= inf +//Objective function to be minimised +function y=f(x) +y=-((x(1)-1)^2+(x(2)-1)^2); +endfunction +//Variable bounds +x1 = [-%inf , -%inf]; +x2 = []; +//Options +options=list("MaxIter",[1500],"CpuTime", [100],"TolX",[1e-6]) +//Calling Ipopt +[x,fval,exitflag,output,lambda] =fminbnd(f, x1, x2, options) + ]]></programlisting> +</refsection> + +<refsection> + <title>Authors</title> + <simplelist type="vert"> + <member>R.Vidyadhar , Vignesh Kannan</member> + </simplelist> +</refsection> +</refentry> |