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

   1 <?xml version="1.0" encoding="ISO-8859-1"?>
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  13 <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"><info><pubdate>$LastChangedDate$</pubdate></info><refnamediv><refname>karmarkar</refname><refpurpose> karmarkar algorithm</refpurpose></refnamediv>
  14
  15
  16
  17
  18
  19   <refsynopsisdiv><title>Calling Sequence</title><synopsis>[x1]=karmarkar(a,b,c,x0)</synopsis></refsynopsisdiv>
  20   <refsection><title>Parameters</title>
  21     <variablelist>
  22       <varlistentry>
  23         <term>a</term>
  24         <listitem>
  25           <para>matrix (n,p)</para>
  26         </listitem>
  27       </varlistentry>
  28       <varlistentry>
  29         <term>b</term>
  30         <listitem>
  31           <para> n - vector</para>
  32         </listitem>
  33       </varlistentry>
  34       <varlistentry>
  35         <term>c</term>
  36         <listitem>
  37           <para> p - vector</para>
  38         </listitem>
  39       </varlistentry>
  40       <varlistentry>
  41         <term>x0</term>
  42         <listitem>
  43           <para> initial vector</para>
  44         </listitem>
  45       </varlistentry>
  46       <varlistentry>
  47         <term>eps</term>
  48         <listitem>
  49           <para>threshold (default value : 1.d-5)</para>
  50         </listitem>
  51       </varlistentry>
  52       <varlistentry>
  53         <term>gamma</term>
  54         <listitem>
  55           <para>descent step  <literal>0&lt;gamma&lt;1</literal> , default value : 1/4</para>
  56         </listitem>
  57       </varlistentry>
  58       <varlistentry>
  59         <term>x1</term>
  60         <listitem>
  61           <para>solution</para>
  62         </listitem>
  63       </varlistentry>
  64       <varlistentry>
  65         <term>crit</term>
  66         <listitem>
  67           <para>value of  c'*x1</para>
  68         </listitem>
  69       </varlistentry>
  70     </variablelist>
  71   </refsection>
  72   <refsection><title>Description</title>
  73     <para>
  74     Computes <literal>x</literal> which minimizes</para>
  75     <programlisting><![CDATA[
  76
  77                         c'*x
  78
  79     ]]></programlisting>
  80     <para>
  81     under constraints:</para>
  82     <programlisting><![CDATA[
  83
  84                         a*x = b
  85                         x>=0
  86
  87     ]]></programlisting>
  88   </refsection>
  89   <refsection><title>Examples</title><programlisting role="example"><![CDATA[
  90
  91 // n=10;p=20;
  92 // a=rand(n,p);c=rand(p,1);x0=abs(rand(p,1));b=a*x0;x1=karmarkar(a,b,c,x0);
  93
  94   ]]></programlisting></refsection>
  95 </refentry>