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<?xml version="1.0" encoding="UTF-8"?>
<!--
*
* This help file was generated from lsqlin.sci using help_from_sci().
*
-->
<refentry version="5.0-subset Scilab" xml:id="lsqlin" 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>lsqlin</refname>
<refpurpose>Solves a linear quadratic problem.</refpurpose>
</refnamediv>
<refsynopsisdiv>
<title>Calling Sequence</title>
<synopsis>
x = lsqlin(C,d,A,b)
x = lsqlin(C,d,A,b,Aeq,beq)
x = lsqlin(C,d,A,b,Aeq,beq,lb,ub)
x = lsqlin(C,d,A,b,Aeq,beq,lb,ub,x0)
x = lsqlin(C,d,A,b,Aeq,beq,lb,ub,x0,param)
[xopt,resnorm,residual,exitflag,output,lambda] = lsqlin( ... )
</synopsis>
</refsynopsisdiv>
<refsection>
<title>Parameters</title>
<variablelist>
<varlistentry><term>C :</term>
<listitem><para> a matrix of doubles, represents the multiplier of the solution x in the expression C*x - d. C is M-by-N, where M is the number of equations, and N is the number of elements of x.</para></listitem></varlistentry>
<varlistentry><term>d :</term>
<listitem><para> a vector of doubles, represents the additive constant term in the expression C*x - d. d is M-by-1, where M is the number of equations.</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, contains lower bounds of the variables.</para></listitem></varlistentry>
<varlistentry><term>UB :</term>
<listitem><para> a vector of doubles, 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>resnorm :</term>
<listitem><para> a double, objective value returned as the scalar value norm(C*x-d)^2.</para></listitem></varlistentry>
<varlistentry><term>residual :</term>
<listitem><para> a vector of doubles, solution residuals returned as the vector C*x-d.</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 least square problem specified by :
</para>
<para>
<latex>
\begin{eqnarray}
&\mbox{min}_{x}
& 1/2||C*x - d||_2^2 \\
& \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 linear least square 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[
//A simple linear least square example
C = [0.9501 0.7620 0.6153 0.4057
0.2311 0.4564 0.7919 0.9354
0.6068 0.0185 0.9218 0.9169
0.4859 0.8214 0.7382 0.4102
0.8912 0.4447 0.1762 0.8936];
d = [0.0578
0.3528
0.8131
0.0098
0.1388];
A = [0.2027 0.2721 0.7467 0.4659
0.1987 0.1988 0.4450 0.4186
0.6037 0.0152 0.9318 0.8462];
b = [0.5251
0.2026
0.6721];
[xopt,resnorm,residual,exitflag,output,lambda] = lsqlin(C,d,A,b)
]]></programlisting>
</refsection>
<refsection>
<title>Examples</title>
<programlisting role="example"><![CDATA[
C = [0.9501 0.7620 0.6153 0.4057
0.2311 0.4564 0.7919 0.9354
0.6068 0.0185 0.9218 0.9169
0.4859 0.8214 0.7382 0.4102
0.8912 0.4447 0.1762 0.8936];
d = [0.0578
0.3528
0.8131
0.0098
0.1388];
A =[0.2027 0.2721 0.7467 0.4659
0.1987 0.1988 0.4450 0.4186
0.6037 0.0152 0.9318 0.8462];
b =[0.5251
0.2026
0.6721];
Aeq = [3 5 7 9];
beq = 4;
lb = -0.1*ones(4,1);
ub = 2*ones(4,1);
[xopt,resnorm,residual,exitflag,output,lambda] = lsqlin(C,d,A,b,Aeq,beq,lb,ub)
]]></programlisting>
</refsection>
<refsection>
<title>Authors</title>
<simplelist type="vert">
<member>Harpreet Singh</member>
</simplelist>
</refsection>
</refentry>
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