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diff --git a/help/en_US/intfminbnd.xml b/help/en_US/intfminbnd.xml new file mode 100644 index 0000000..dbc8fa9 --- /dev/null +++ b/help/en_US/intfminbnd.xml @@ -0,0 +1,242 @@ +<?xml version="1.0" encoding="UTF-8"?> + +<!-- + * + * This help file was generated from intfminbnd.sci using help_from_sci(). + * + --> + +<refentry version="5.0-subset Scilab" xml:id="intfminbnd" 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>intfminbnd</refname> + <refpurpose>Solves a multi-variable optimization problem on a bounded interval</refpurpose> + </refnamediv> + + +<refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis> + xopt = intfminbnd(f,intcon,x1,x2) + xopt = intfminbnd(f,intcon,x1,x2,options) + [xopt,fopt] = intfminbnd(.....) + [xopt,fopt,exitflag]= intfminbnd(.....) + [xopt,fopt,exitflag,output]=intfminbnd(.....) + [xopt,fopt,exitflag,gradient,hessian]=intfminbnd(.....) + + </synopsis> +</refsynopsisdiv> + +<refsection> + <title>Input Parameters</title> + <variablelist> + <varlistentry><term>f :</term> + <listitem><para> A function, representing the objective function of the problem.</para></listitem></varlistentry> + <varlistentry><term><latex>x_{1}</latex> :</term> + <listitem><para> A vector, containing the lower bound of the variables of size (1 X n) or (n X 1) where n is number of variables. If it is empty it means that the lower bound is <latex>-\infty</latex>.</para></listitem></varlistentry> + <varlistentry><term><latex>x_{2}</latex> :</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 it is empty it means that the upper bound is <latex>\infty</latex>.</para></listitem></varlistentry> + <varlistentry><term>intcon :</term> + <listitem><para> A vector of integers, representing the variables that are constrained to be integers.</para></listitem></varlistentry> + <varlistentry><term>options :</term> + <listitem><para> A list, containing the options for user to specify. See below for details.</para></listitem></varlistentry> + </variablelist> +</refsection> + <refsection> +<title> Outputs</title> + <variablelist> + <varlistentry><term>xopt :</term> + <listitem><para> A vector of doubles, containing the computed solution of the optimization problem.</para></listitem></varlistentry> + <varlistentry><term>fopt :</term> + <listitem><para> A double, containing the the function value at x.</para></listitem></varlistentry> + <varlistentry><term>exitflag :</term> + <listitem><para> An integer, containing the flag which denotes the reason for termination of algorithm. See below for details.</para></listitem></varlistentry> + <varlistentry><term>gradient :</term> + <listitem><para> A vector of doubles, containing the objective's gradient of the solution.</para></listitem></varlistentry> + <varlistentry><term>hessian :</term> + <listitem><para>A matrix of doubles, containing the Lagrangian's hessian of the solution.</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{Subjected to:}\\ & x_{1} \ < x \ < x_{2} \\ +\end{eqnarray} +</latex> + </para> + <para> +intfminbnd calls Bonmin, which is an optimization library written in C++, to solve the bound optimization problem. + </para> + <para> +<title>Options</title> +The options allow the user to set various parameters of the Optimization problem. The syntax for the options is given by: + </para> + <para> +options= list("IntegerTolerance", [---], "MaxNodes",[---], "MaxIter", [---], "AllowableGap",[---] "CpuTime", [---],"gradobj", "off", "hessian", "off" ); +<itemizedlist> +<listitem>IntegerTolerance : A Scalar, a number with that value of an integer is considered integer.</listitem> +<listitem>MaxNodes : A Scalar, containing the maximum number of nodes that the solver should search.</listitem> +<listitem>CpuTime : A scalar, specifying the maximum amount of CPU Time in seconds that the solver should take.</listitem> +<listitem>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.</listitem> +<listitem>MaxIter : A scalar, specifying the maximum number of iterations that the solver should take.</listitem> +<listitem>gradobj : A string, to turn on or off the user supplied objective gradient.</listitem> +<listitem>hessian : A scalar, to turn on or off the user supplied objective hessian.</listitem> +</itemizedlist> + The default values for the various items are given as: + </para> + <para> + options = list('integertolerance',1d-06,'maxnodes',2147483647,'cputime',1d10,'allowablegap',0,'maxiter',2147483647,'gradobj',"off",'hessian',"off") + </para> + + <para> +The exitflag allows the user to know the status of the optimization which is returned by Bonmin. The values it can take and what they indicate is described below: +<itemizedlist> +<listitem> 0 : Optimal Solution Found </listitem> +<listitem> 1 : Maximum Number of Iterations Exceeded. Output may not be optimal.</listitem> +<listitem> 2 : Maximum amount of CPU Time exceeded. Output may not be optimal.</listitem> +<listitem> 3 : Stop at Tiny Step.</listitem> +<listitem> 4 : Solved To Acceptable Level.</listitem> +<listitem> 5 : Converged to a point of local infeasibility.</listitem> +</itemizedlist> + </para> + <para> +For more details on exitflag, see the Bonmin documentation which can be found on http://www.coin-or.org/Bonmin + </para> + <para> +</para> +</refsection> +<para> +A few examples displaying the various functionalities of intfminbnd have been provided below. You will find a series of problems and the appropriate code snippets to solve them. + </para> +<refsection> + <title>Example</title> + <para> +We start with a simple objective function. Find x in R^6 such that it minimizes: + </para> + <para> +<latex> +\begin{eqnarray} +\mbox{min}_{x}\ f(x) = sin(x_{1}) + sin(x_{2}) + sin(x_{3}) + sin(x_{4}) + sin(x_{5}) + sin(x_{6}) +\end{eqnarray} +\\\text{Subjected to:}\\ +\begin{eqnarray} +\hspace{70pt} &-2 &\leq x{1}, x{2}, x{3}, x{4}, x{5}, x{6} &\leq 2\\ +\end{eqnarray}\\ +\text{With integer constraints as: }\\ +\begin{eqnarray} +\begin{array}{ccc} +[2 & 3 & 4] \\ +\end{array} +\end{eqnarray} +</latex> + </para> +<para> +</para> + <programlisting role="example"><![CDATA[ +//Example 1: +//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]; +intcon = [2 3 4] +[x,fval] =intfminbnd(f ,intcon, x1, x2) +// Press ENTER to continue + + ]]></programlisting> +</refsection> + +<refsection> + <title>Example</title> + Here we solve a bounded objective function in R^6. We use this function to illustrate how we can further enhance the functionality of fminbnd 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. + <programlisting role="example"><![CDATA[ +//Example 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]; +intcon = [2 3 4] +//Options +options=list("MaxIter",[1500],"CpuTime", [100]) +[x,fval] =intfminbnd(f ,intcon, x1, x2, options) +// Press ENTER to continue + + ]]></programlisting> +</refsection> + + +<refsection> + <title>Example</title> + <para> + Unbounded Problems: Find x in R^2 such that it minimizes: + </para> + <para> + <latex> + \begin{eqnarray} +f(x) = -((x_{1}-1)^{2}+(x_{2}-1)^{2}) +\end{eqnarray} +\\\text{Subjected to:}\\ +\begin{eqnarray} +-\infty &\leq x_{1} &\leq \infty\\ +-\infty &\leq x_{2} &\leq \infty +\end{eqnarray}\\ +\text{With integer constraints as: } \\ +\begin{eqnarray} +\begin{array}{cccccc} +[1 & 2] \\ +\end{array} +\end{eqnarray} +</latex> +</para> +<para> +</para> + <programlisting role="example"><![CDATA[ +///Example 3: Unbounded problem: +//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 = [ %inf , %inf]; +//Options +options=list("MaxIter",[1500],"CpuTime", [100]); +intcon = [1 2]; +[x,fval,exitflag,output,lambda] =intfminbnd(f,intcon, x1, x2, options) + ]]></programlisting> +</refsection> + +<refsection> + <title>Authors</title> + <simplelist type="vert"> + <member>Harpreet Singh</member> + </simplelist> +</refsection> +</refentry> |