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

   1 <?xml version="1.0" encoding="ISO-8859-1" standalone="no"?>
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   4  * Copyright (C) 2008 - INRIA
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   7  * This source file is licensed as described in the file COPYING, which
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  10  * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
  11  *
  12  -->
  13 <!DOCTYPE MAN SYSTEM "../../../../modules/helptools/help.dtd">
  14 <MAN>
  15   <LANGUAGE>eng</LANGUAGE>
  16   <TITLE>karmarkar</TITLE>
  17   <TYPE>Scilab Function</TYPE>
  18   <DATE>$LastChangedDate$</DATE>
  19   <SHORT_DESCRIPTION name="karmarkar"> karmarkar algorithm</SHORT_DESCRIPTION>
  20   <CALLING_SEQUENCE>
  21     <CALLING_SEQUENCE_ITEM>[x1]=karmarkar(a,b,c,x0)  </CALLING_SEQUENCE_ITEM>
  22   </CALLING_SEQUENCE>
  23   <PARAM>
  24     <PARAM_INDENT>
  25       <PARAM_ITEM>
  26         <PARAM_NAME>a</PARAM_NAME>
  27         <PARAM_DESCRIPTION>
  28           <SP>: matrix (n,p)</SP>
  29         </PARAM_DESCRIPTION>
  30       </PARAM_ITEM>
  31       <PARAM_ITEM>
  32         <PARAM_NAME>b</PARAM_NAME>
  33         <PARAM_DESCRIPTION>
  34           <SP>:  n - vector</SP>
  35         </PARAM_DESCRIPTION>
  36       </PARAM_ITEM>
  37       <PARAM_ITEM>
  38         <PARAM_NAME>c</PARAM_NAME>
  39         <PARAM_DESCRIPTION>
  40           <SP>:  p - vector</SP>
  41         </PARAM_DESCRIPTION>
  42       </PARAM_ITEM>
  43       <PARAM_ITEM>
  44         <PARAM_NAME>x0</PARAM_NAME>
  45         <PARAM_DESCRIPTION>
  46           <SP>:  initial vector</SP>
  47         </PARAM_DESCRIPTION>
  48       </PARAM_ITEM>
  49       <PARAM_ITEM>
  50         <PARAM_NAME>eps</PARAM_NAME>
  51         <PARAM_DESCRIPTION>
  52           <SP>: threshold (default value : 1.d-5)</SP>
  53         </PARAM_DESCRIPTION>
  54       </PARAM_ITEM>
  55       <PARAM_ITEM>
  56         <PARAM_NAME>gamma</PARAM_NAME>
  57         <PARAM_DESCRIPTION>
  58           <SP>: descent step  <VERB>0&lt;gamma&lt;1</VERB> , default value : 1/4</SP>
  59         </PARAM_DESCRIPTION>
  60       </PARAM_ITEM>
  61       <PARAM_ITEM>
  62         <PARAM_NAME>x1</PARAM_NAME>
  63         <PARAM_DESCRIPTION>
  64           <SP>: solution</SP>
  65         </PARAM_DESCRIPTION>
  66       </PARAM_ITEM>
  67       <PARAM_ITEM>
  68         <PARAM_NAME>crit</PARAM_NAME>
  69         <PARAM_DESCRIPTION>
  70           <SP>: value of  c'*x1</SP>
  71         </PARAM_DESCRIPTION>
  72       </PARAM_ITEM>
  73     </PARAM_INDENT>
  74   </PARAM>
  75   <DESCRIPTION>
  76     <P>
  77     Computes <VERB>x</VERB> which minimizes</P>
  78     <VERBATIM>
  79 <![CDATA[
  80                         c'*x
  81    ]]>
  82     </VERBATIM>
  83     <P>
  84     under constraints:</P>
  85     <VERBATIM>
  86 <![CDATA[
  87                         a*x = b
  88                         x>=0
  89    ]]>
  90     </VERBATIM>
  91   </DESCRIPTION>
  92   <EXAMPLE>
  93 <![CDATA[
  94 // n=10;p=20;
  95 // a=rand(n,p);c=rand(p,1);x0=abs(rand(p,1));b=a*x0;x1=karmarkar(a,b,c,x0);
  96  ]]>
  97   </EXAMPLE>
  98 </MAN>