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diff --git a/help/en_US/intfminunc.xml b/help/en_US/intfminunc.xml new file mode 100644 index 0000000..df2cdda --- /dev/null +++ b/help/en_US/intfminunc.xml @@ -0,0 +1,242 @@ +<?xml version="1.0" encoding="UTF-8"?> + +<!-- + * + * This help file was generated from intfminunc.sci using help_from_sci(). + * + --> + +<refentry version="5.0-subset Scilab" xml:id="intfminunc" 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>intfminunc</refname> + <refpurpose>Solves an unconstrainted multi-variable mixed integer non linear programming optimization problem</refpurpose> + </refnamediv> + + +<refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis> + xopt = intfminunc(f,x0) + xopt = intfminunc(f,x0,intcon) + xopt = intfminunc(f,x0,intcon,options) + [xopt,fopt] = intfminunc(.....) + [xopt,fopt,exitflag]= intfminunc(.....) + [xopt,fopt,exitflag,gradient,hessian]= intfminunc(.....) + + </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>x0 :</term> + <listitem><para> A vector of doubles, containing the starting values of variables of size (1 X n) or (n X 1) where 'n' is the number of Variables.</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 option 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 mixed integer non linear programming unconstrained optimization problem specified by : +Find the minimum of f(x) such that + </para> + <para> +<latex> +\begin{eqnarray} +&\mbox{min}_{x} +& f(x) +& x_{i} \in \!\, \mathbb{Z}, i \in \!\, I +\end{eqnarray} +</latex> + </para> + <para> +intfminunc 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> + </para> + <para> +The exitflag allows to know the status of the optimization which is given back by Ipopt. +<itemizedlist> +<listitem>0 : Optimal Solution Found </listitem> +<listitem>1 : InFeasible Solution.</listitem> +<listitem>2 : Objective Function is Continuous Unbounded.</listitem> +<listitem>3 : Limit Exceeded.</listitem> +<listitem>4 : User Interrupt.</listitem> +<listitem>5 : MINLP Error.</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 intfminunc 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 begin with the minimization of a simple non-linear function. +</para> + <para> +Find x in R^2 such that it minimizes: + </para> + <para> +<latex> +\begin{eqnarray} +\mbox{min}_{x}\ f(x) = x_{1}^{2} + x_{2}^{2} +\end{eqnarray}\\ +\text{With integer constraints as: } \\ +\begin{eqnarray} +\begin{array}{c} +[1] \\ +\end{array} +\end{eqnarray} +</latex> + </para> + <para> + </para> + <programlisting role="example"><![CDATA[ +//Example 1: +//Objective function to be minimised +function y= f(x) +y= x(1)^2 + x(2)^2; +endfunction +//Starting point +x0=[2,1]; +intcon = [1]; +[xopt,fopt]=intfminunc(f,x0,intcon) +// Press ENTER to continue + + ]]></programlisting> +</refsection> + +<refsection> + <title>Example</title> + <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. +</para> + <para> +<latex> +\begin{eqnarray} +\mbox{min}_{x}\ f(x) = 100\boldsymbol{\cdot} (x_{2} - x_{1}^{2})^{2} + (1-x_{1})^{2} +\end{eqnarray}\\ +\text{With integer constraints as: } \\ +\begin{eqnarray} +\begin{array}{c} +[2] \\ +\end{array} +\end{eqnarray} +</latex> + </para> + <para> + </para> + <programlisting role="example"><![CDATA[ +///Example 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]; +intcon = [2] +//Options +options=list("MaxIter", [1500], "CpuTime", [500]); +//Calling +[xopt,fopt,exitflag,gradient,hessian]=intfminunc(f,x0,intcon,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}^{2} - x_{2}^{2} +\end{eqnarray}\\ +\text{With integer constraints as: } \\ +\begin{eqnarray} +\begin{array}{c} +[1] \\ +\end{array} +\end{eqnarray} +</latex> + </para> + <para> + </para> + <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,g,h] = f(x) +y = -x(1)^2 - x(2)^2; +g = [-2*x(1),-2*x(2)]; +h = [-2,0;0,-2]; +endfunction +//Starting point +x0=[2,1]; +intcon = [1] +options = list("gradobj","ON","hessian","on"); +[xopt,fopt,exitflag,gradient,hessian]=intfminunc(f,x0,intcon,options) + ]]></programlisting> +</refsection> +</refentry> |