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diff --git a/help/en_US/qpipopt_mat.xml b/help/en_US/qpipopt_mat.xml new file mode 100644 index 0000000..7dec2b1 --- /dev/null +++ b/help/en_US/qpipopt_mat.xml @@ -0,0 +1,142 @@ +<?xml version="1.0" encoding="UTF-8"?> + +<!-- + * + * This help file was generated from qpipopt_mat.sci using help_from_sci(). + * + --> + +<refentry version="5.0-subset Scilab" xml:id="qpipopt_mat" 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>qpipopt_mat</refname> + <refpurpose>Solves a linear quadratic problem.</refpurpose> + </refnamediv> + + +<refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis> + xopt = qpipopt_mat(nbVar,nbCon,Q,p,LB,UB,conMatrix,conLB,conUB) + x = qpipopt_mat(H,f) + x = qpipopt_mat(H,f,A,b) + x = qpipopt_mat(H,f,A,b,Aeq,beq) + x = qpipopt_mat(H,f,A,b,Aeq,beq,lb,ub) + [xopt,fopt,exitflag,output,lamda] = qpipopt_mat( ... ) + + </synopsis> +</refsynopsisdiv> + +<refsection> + <title>Parameters</title> + <variablelist> + <varlistentry><term>H :</term> + <listitem><para> a n x n matrix of doubles, where n is number of variables, represents coefficients of quadratic in the quadratic problem.</para></listitem></varlistentry> + <varlistentry><term>f :</term> + <listitem><para> a n x 1 matrix of doubles, where n is number of variables, represents coefficients of linear in the quadratic problem</para></listitem></varlistentry> + <varlistentry><term>A :</term> + <listitem><para> a m x n matrix of doubles, represents the linear coefficients in the inequality constraints</para></listitem></varlistentry> + <varlistentry><term>b :</term> + <listitem><para> a column vector of doubles, represents the linear coefficients in the inequality constraints</para></listitem></varlistentry> + <varlistentry><term>Aeq :</term> + <listitem><para> a meq x n matrix of doubles, represents the linear coefficients in the equality constraints</para></listitem></varlistentry> + <varlistentry><term>beq :</term> + <listitem><para> a vector of doubles, represents the linear coefficients in the equality constraints</para></listitem></varlistentry> + <varlistentry><term>LB :</term> + <listitem><para> a n x 1 matrix of doubles, where n is number of variables, contains lower bounds of the variables.</para></listitem></varlistentry> + <varlistentry><term>UB :</term> + <listitem><para> a n x 1 matrix of doubles, where n is number of variables, contains upper bounds of the variables.</para></listitem></varlistentry> + <varlistentry><term>xopt :</term> + <listitem><para> a nx1 matrix of doubles, the computed solution of the optimization problem.</para></listitem></varlistentry> + <varlistentry><term>fopt :</term> + <listitem><para> a 1x1 matrix of doubles, the function value at x.</para></listitem></varlistentry> + <varlistentry><term>exitflag :</term> + <listitem><para> Integer identifying the reason the algorithm terminated.</para></listitem></varlistentry> + <varlistentry><term>output :</term> + <listitem><para> Structure containing information about the optimization.</para></listitem></varlistentry> + <varlistentry><term>lambda :</term> + <listitem><para> Structure containing the Lagrange multipliers at the solution x (separated by constraint type).</para></listitem></varlistentry> + </variablelist> +</refsection> + +<refsection> + <title>Description</title> + <para> +Search the minimum of a constrained linear quadratic optimization problem specified by : +find the minimum of f(x) such that + </para> + <para> +<latex> +\begin{eqnarray} +&\mbox{min}_{x} +& 1/2*x'*H*x + f'*x \\ +& \text{subject to} & A.x \leq b \\ +& & Aeq.x \leq beq \\ +& & lb \leq x \leq ub \\ +\end{eqnarray} +</latex> + </para> + <para> +We are calling IPOpt for solving the quadratic problem, IPOpt is a library written in C++. The code has been written by Andreas Wächter and Carl Laird. + </para> + <para> +</para> +</refsection> + +<refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +//Find x in R^6 such that: + +Aeq= [1,-1,1,0,3,1; +-1,0,-3,-4,5,6; +2,5,3,0,1,0]; +beq=[1; 2; 3]; +A= [0,1,0,1,2,-1; +-1,0,2,1,1,0]; +b = [-1; 2.5]; +lb=[-1000; -10000; 0; -1000; -1000; -1000]; +ub=[10000; 100; 1.5; 100; 100; 1000]; +//and minimize 0.5*x'*Q*x + p'*x with +f=[1; 2; 3; 4; 5; 6]; H=eye(6,6); +[xopt,fopt,exitflag,output,lambda]=qpipopt_mat(H,f,A,b,Aeq,beq,lb,ub) +clear H f A b Aeq beq lb ub; + + ]]></programlisting> +</refsection> + +<refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +//Find the value of x that minimize following function +// f(x) = 0.5*x1^2 + x2^2 - x1*x2 - 2*x1 - 6*x2 +// Subject to: +// x1 + x2 ≤ 2 +// –x1 + 2x2 ≤ 2 +// 2x1 + x2 ≤ 3 +// 0 ≤ x1, 0 ≤ x2. +H = [1 -1; -1 2]; +f = [-2; -6]; +A = [1 1; -1 2; 2 1]; +b = [2; 2; 3]; +lb = [0; 0]; +ub = [%inf; %inf]; +[xopt,fopt,exitflag,output,lambda] = qpipopt_mat(H,f,A,b,[],[],lb,ub) + + ]]></programlisting> +</refsection> + +<refsection> + <title>Authors</title> + <simplelist type="vert"> + <member>Keyur Joshi, Saikiran, Iswarya, Harpreet Singh</member> + </simplelist> +</refsection> +</refentry> |