-<?xml version="1.0" encoding="ISO-8859-1"?>
+<?xml version="1.0" encoding="UTF-8"?>
<!--
* Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
* Copyright (C) 2008 - INRIA
* http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
*
-->
-<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" version="5.0-subset Scilab" xml:lang="en" xml:id="karmarkar">
+<refentry version="5.0-subset Scilab" xml:id="karmarkar" 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:ns4="http://www.w3.org/1999/xhtml"
+ xmlns:mml="http://www.w3.org/1998/Math/MathML"
+ xmlns:db="http://docbook.org/ns/docbook">
<info>
<pubdate>$LastChangedDate$</pubdate>
</info>
+
<refnamediv>
<refname>karmarkar</refname>
- <refpurpose> karmarkar algorithm</refpurpose>
+
+ <refpurpose>karmarkar algorithm</refpurpose>
</refnamediv>
+
<refsynopsisdiv>
<title>Calling Sequence</title>
+
<synopsis>[x1]=karmarkar(a,b,c,x0)</synopsis>
</refsynopsisdiv>
+
<refsection>
<title>Parameters</title>
+
<variablelist>
<varlistentry>
<term>a</term>
+
<listitem>
<para>matrix (n,p)</para>
</listitem>
</varlistentry>
+
<varlistentry>
<term>b</term>
+
<listitem>
- <para> n - vector</para>
+ <para>n - vector</para>
</listitem>
</varlistentry>
+
<varlistentry>
<term>c</term>
+
<listitem>
- <para> p - vector</para>
+ <para>p - vector</para>
</listitem>
</varlistentry>
+
<varlistentry>
<term>x0</term>
+
<listitem>
- <para> initial vector</para>
+ <para>initial vector</para>
</listitem>
</varlistentry>
+
<varlistentry>
<term>eps</term>
+
<listitem>
<para>threshold (default value : 1.d-5)</para>
</listitem>
</varlistentry>
+
<varlistentry>
<term>gamma</term>
+
<listitem>
- <para>descent step <literal>0<gamma<1</literal> , default value : 1/4</para>
+ <para>descent step <literal>0<gamma<1</literal> , default
+ value : 1/4</para>
</listitem>
</varlistentry>
+
<varlistentry>
<term>x1</term>
+
<listitem>
<para>solution</para>
</listitem>
</varlistentry>
+
<varlistentry>
<term>crit</term>
+
<listitem>
- <para>value of c'*x1</para>
+ <para>value of c'*x1</para>
</listitem>
</varlistentry>
</variablelist>
</refsection>
+
<refsection>
<title>Description</title>
- <para>
- Computes <literal>x</literal> which minimizes</para>
- <programlisting><![CDATA[
-
- c'*x
-
- ]]></programlisting>
- <para>
- under constraints:</para>
- <programlisting><![CDATA[
-
- a*x = b
- x>=0
-
- ]]></programlisting>
+
+ <para>Computes <literal>x</literal> which minimizes</para>
+
+ <informalequation>
+ <mediaobject>
+ <imageobject>
+ <imagedata align="center" fileref="../mml/karmarkar_equation_1.mml" />
+ </imageobject>
+ </mediaobject>
+ </informalequation>
</refsection>
+
<refsection>
<title>Examples</title>
- <programlisting role="example"><![CDATA[
-// n=10;p=20;
-// a=rand(n,p);c=rand(p,1);x0=abs(rand(p,1));b=a*x0;x1=karmarkar(a,b,c,x0);
-
- ]]></programlisting>
+ <programlisting role="example"><![CDATA[
+n=10;p=20;
+a=rand(n,p);
+c=rand(p,1);
+x0=abs(rand(p,1));
+b=a*x0;
+x1=karmarkar(a,b,c,x0);
+ ]]></programlisting>
</refsection>
</refentry>