scilab/modules/optimization/help/en_US/karmarkar.xml

   1 <?xml version="1.0" encoding="UTF-8"?>
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  13 <refentry version="5.0-subset Scilab" xml:id="karmarkar" xml:lang="en"
  14           xmlns="http://docbook.org/ns/docbook"
  15           xmlns:xlink="http://www.w3.org/1999/xlink"
  16           xmlns:svg="http://www.w3.org/2000/svg"
  17           xmlns:ns4="http://www.w3.org/1999/xhtml"
  18           xmlns:mml="http://www.w3.org/1998/Math/MathML"
  19           xmlns:db="http://docbook.org/ns/docbook">
  20   <info>
  21     <pubdate>$LastChangedDate$</pubdate>
  22   </info>
  23
  24   <refnamediv>
  25     <refname>karmarkar</refname>
  26
  27     <refpurpose>karmarkar algorithm</refpurpose>
  28   </refnamediv>
  29
  30   <refsynopsisdiv>
  31     <title>Calling Sequence</title>
  32
  33     <synopsis>[x1]=karmarkar(a,b,c,x0)</synopsis>
  34   </refsynopsisdiv>
  35
  36   <refsection>
  37     <title>Parameters</title>
  38
  39     <variablelist>
  40       <varlistentry>
  41         <term>a</term>
  42
  43         <listitem>
  44           <para>matrix (n,p)</para>
  45         </listitem>
  46       </varlistentry>
  47
  48       <varlistentry>
  49         <term>b</term>
  50
  51         <listitem>
  52           <para>n - vector</para>
  53         </listitem>
  54       </varlistentry>
  55
  56       <varlistentry>
  57         <term>c</term>
  58
  59         <listitem>
  60           <para>p - vector</para>
  61         </listitem>
  62       </varlistentry>
  63
  64       <varlistentry>
  65         <term>x0</term>
  66
  67         <listitem>
  68           <para>initial vector</para>
  69         </listitem>
  70       </varlistentry>
  71
  72       <varlistentry>
  73         <term>eps</term>
  74
  75         <listitem>
  76           <para>threshold (default value : 1.d-5)</para>
  77         </listitem>
  78       </varlistentry>
  79
  80       <varlistentry>
  81         <term>gamma</term>
  82
  83         <listitem>
  84           <para>descent step <literal>0&lt;gamma&lt;1</literal> , default
  85           value : 1/4</para>
  86         </listitem>
  87       </varlistentry>
  88
  89       <varlistentry>
  90         <term>x1</term>
  91
  92         <listitem>
  93           <para>solution</para>
  94         </listitem>
  95       </varlistentry>
  96
  97       <varlistentry>
  98         <term>crit</term>
  99
 100         <listitem>
 101           <para>value of c'*x1</para>
 102         </listitem>
 103       </varlistentry>
 104     </variablelist>
 105   </refsection>
 106
 107   <refsection>
 108     <title>Description</title>
 109
 110     <para>Computes <literal>x</literal> which minimizes</para>
 111
 112     <informalequation>
 113       <mediaobject>
 114         <imageobject>
 115           <imagedata align="center" fileref="../mml/karmarkar_equation_1.mml" />
 116         </imageobject>
 117       </mediaobject>
 118     </informalequation>
 119   </refsection>
 120
 121   <refsection>
 122     <title>Examples</title>
 123
 124     <programlisting role="example"><![CDATA[
 125 n=10;p=20;
 126 a=rand(n,p);
 127 c=rand(p,1);
 128 x0=abs(rand(p,1));
 129 b=a*x0;
 130 x1=karmarkar(a,b,c,x0);
 131  ]]></programlisting>
 132   </refsection>
 133 </refentry>