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<?xml version="1.0" encoding="UTF-8"?>
<!--
*
* This help file was generated from qpipoptmat.sci using help_from_sci().
*
-->
<refentry version="5.0-subset Scilab" xml:id="qpipoptmat" 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>qpipoptmat</refname>
<refpurpose>Solves a linear quadratic problem.</refpurpose>
</refnamediv>
<refsynopsisdiv>
<title>Calling Sequence</title>
<synopsis>
x = qpipoptmat(H,f)
x = qpipoptmat(H,f,A,b)
x = qpipoptmat(H,f,A,b,Aeq,beq)
x = qpipoptmat(H,f,A,b,Aeq,beq,lb,ub)
x = qpipoptmat(H,f,A,b,Aeq,beq,lb,ub,x0)
x = qpipoptmat(H,f,A,b,Aeq,beq,lb,ub,x0,param)
[xopt,fopt,exitflag,output,lamda] = qpipoptmat( ... )
</synopsis>
</refsynopsisdiv>
<refsection>
<title>Parameters</title>
<variablelist>
<varlistentry><term>H :</term>
<listitem><para> a vector 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 vector 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 vector of doubles, represents the linear coefficients in the inequality constraints</para></listitem></varlistentry>
<varlistentry><term>b :</term>
<listitem><para> a vector of doubles, represents the linear coefficients in the inequality constraints</para></listitem></varlistentry>
<varlistentry><term>Aeq :</term>
<listitem><para> a 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 vector of doubles, where n is number of variables, contains lower bounds of the variables.</para></listitem></varlistentry>
<varlistentry><term>UB :</term>
<listitem><para> a vector of doubles, where n is number of variables, contains upper bounds of the variables.</para></listitem></varlistentry>
<varlistentry><term>x0 :</term>
<listitem><para> a vector of doubles, contains initial guess of variables.</para></listitem></varlistentry>
<varlistentry><term>param :</term>
<listitem><para> a list containing the the parameters to be set.</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 double, 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];
x0 = repmat(0,6,1);
param = list("MaxIter", 300, "CpuTime", 100);
//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]=qpipoptmat(H,f,A,b,Aeq,beq,lb,ub,[],param)
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] = qpipoptmat(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>
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