summaryrefslogtreecommitdiff
path: root/help/en_US/scilab_en_US_help/intqpipopt.html
blob: b1c4735e87e07f4754cb6f1405a7606cc6c766a3 (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
<html><head>
    <meta http-equiv="Content-Type" content="text/html; charset=utf-8">
    <title>intqpipopt</title>
    <style type="text/css" media="all">
      @import url("scilab_code.css");
      @import url("xml_code.css");
      @import url("c_code.css");
      @import url("style.css");
    </style>
  </head>
  <body>
    <div class="manualnavbar">
    <table width="100%"><tr>
      <td width="30%">
    	<span class="previous"><a href="intfminunc.html">&lt;&lt; intfminunc</a></span>

      </td>
      <td width="40%" class="center">
      	<span class="top"><a href="section_2f30ec7805b02b8760d8add3187208be.html">FOSSEE Optimization Toolbox</a></span>

      </td>
      <td width="30%" class="next">
      	
      </td>
    </tr></table>
      <hr />
    </div>



    <span class="path"><a href="index.html">FOSSEE Optimization Toolbox</a> &gt;&gt; <a href="section_2f30ec7805b02b8760d8add3187208be.html">FOSSEE Optimization Toolbox</a> &gt; intqpipopt</span>

    <br /><br />
    <div class="refnamediv"><h1 class="refname">intqpipopt</h1>
    <p class="refpurpose">Solves a linear quadratic problem.</p></div>


<div class="refsynopsisdiv"><h3 class="title">Calling Sequence</h3>
   <div class="synopsis"><pre><span class="default">xopt</span><span class="default"> = </span><span class="functionid">intqpipopt</span><span class="default">(</span><span class="default">H</span><span class="default">,</span><span class="default">f</span><span class="default">)</span>
<span class="default">xopt</span><span class="default"> = </span><span class="functionid">intqpipopt</span><span class="default">(</span><span class="default">H</span><span class="default">,</span><span class="default">f</span><span class="default">,</span><span class="default">intcon</span><span class="default">)</span>
<span class="default">xopt</span><span class="default"> = </span><span class="functionid">intqpipopt</span><span class="default">(</span><span class="default">H</span><span class="default">,</span><span class="default">f</span><span class="default">,</span><span class="default">intcon</span><span class="default">,</span><span class="default">A</span><span class="default">,</span><span class="default">b</span><span class="default">)</span>
<span class="default">xopt</span><span class="default"> = </span><span class="functionid">intqpipopt</span><span class="default">(</span><span class="default">H</span><span class="default">,</span><span class="default">f</span><span class="default">,</span><span class="default">intcon</span><span class="default">,</span><span class="default">A</span><span class="default">,</span><span class="default">b</span><span class="default">,</span><span class="default">Aeq</span><span class="default">,</span><span class="default">beq</span><span class="default">)</span>
<span class="default">xopt</span><span class="default"> = </span><span class="functionid">intqpipopt</span><span class="default">(</span><span class="default">H</span><span class="default">,</span><span class="default">f</span><span class="default">,</span><span class="default">intcon</span><span class="default">,</span><span class="default">A</span><span class="default">,</span><span class="default">b</span><span class="default">,</span><span class="default">Aeq</span><span class="default">,</span><span class="default">beq</span><span class="default">,</span><span class="default">lb</span><span class="default">,</span><span class="default">ub</span><span class="default">)</span>
<span class="default">xopt</span><span class="default"> = </span><span class="functionid">intqpipopt</span><span class="default">(</span><span class="default">H</span><span class="default">,</span><span class="default">f</span><span class="default">,</span><span class="default">intcon</span><span class="default">,</span><span class="default">A</span><span class="default">,</span><span class="default">b</span><span class="default">,</span><span class="default">Aeq</span><span class="default">,</span><span class="default">beq</span><span class="default">,</span><span class="default">lb</span><span class="default">,</span><span class="default">ub</span><span class="default">,</span><span class="default">x0</span><span class="default">)</span>
<span class="default">xopt</span><span class="default"> = </span><span class="functionid">intqpipopt</span><span class="default">(</span><span class="default">H</span><span class="default">,</span><span class="default">f</span><span class="default">,</span><span class="default">intcon</span><span class="default">,</span><span class="default">A</span><span class="default">,</span><span class="default">b</span><span class="default">,</span><span class="default">Aeq</span><span class="default">,</span><span class="default">beq</span><span class="default">,</span><span class="default">lb</span><span class="default">,</span><span class="default">ub</span><span class="default">,</span><span class="default">x0</span><span class="default">,</span><span class="default">options</span><span class="default">)</span>
<span class="default">xopt</span><span class="default"> = </span><span class="functionid">intqpipopt</span><span class="default">(</span><span class="default">H</span><span class="default">,</span><span class="default">f</span><span class="default">,</span><span class="default">intcon</span><span class="default">,</span><span class="default">A</span><span class="default">,</span><span class="default">b</span><span class="default">,</span><span class="default">Aeq</span><span class="default">,</span><span class="default">beq</span><span class="default">,</span><span class="default">lb</span><span class="default">,</span><span class="default">ub</span><span class="default">,</span><span class="default">x0</span><span class="default">,</span><span class="default">options</span><span class="default">,</span>&#0034;<span class="default">file_path</span>&#0034;<span class="default">)</span>
<span class="default">[</span><span class="default">xopt</span><span class="default">,</span><span class="default">fopt</span><span class="default">,</span><span class="default">exitflag</span><span class="default">,</span><span class="default">output</span><span class="default">] = </span><span class="functionid">intqpipopt</span><span class="default">( ... )</span></pre></div></div>

<div class="refsection"><h3 class="title">Parameters</h3>
   <dl><dt><span class="term">H :</span>
      <dd><p class="para">a symmetric matrix of double, represents coefficients of quadratic in the quadratic problem.</p></dd></dt>
   <dt><span class="term">f :</span>
      <dd><p class="para">a vector of double, represents coefficients of linear in the quadratic problem</p></dd></dt>
   <dt><span class="term">intcon :</span>
      <dd><p class="para">a vector of integers, represents which variables are constrained to be integers</p></dd></dt>
   <dt><span class="term">A :</span>
      <dd><p class="para">a matrix of double, represents the linear coefficients in the inequality constraints A⋅x ≤ b.</p></dd></dt>
   <dt><span class="term">b :</span>
      <dd><p class="para">a vector of double, represents the linear coefficients in the inequality constraints A⋅x ≤ b.</p></dd></dt>
   <dt><span class="term">Aeq :</span>
      <dd><p class="para">a matrix of double, represents the linear coefficients in the equality constraints Aeq⋅x = beq.</p></dd></dt>
   <dt><span class="term">beq :</span>
      <dd><p class="para">a vector of double, represents the linear coefficients in the equality constraints Aeq⋅x = beq.</p></dd></dt>
   <dt><span class="term">lb :</span>
      <dd><p class="para">a vector of double, contains lower bounds of the variables.</p></dd></dt>
   <dt><span class="term">ub :</span>
      <dd><p class="para">a vector of double, contains upper bounds of the variables.</p></dd></dt>
   <dt><span class="term">x0 :</span>
      <dd><p class="para">a vector of double, contains initial guess of variables.</p></dd></dt>
   <dt><span class="term">options :</span>
      <dd><p class="para">a list containing the parameters to be set.</p></dd></dt>
   <dt><span class="term">file_path :</span>
      <dd><p class="para">path to bonmin opt file if used.</p></dd></dt>
   <dt><span class="term">xopt :</span>
      <dd><p class="para">a vector of double, the computed solution of the optimization problem.</p></dd></dt>
   <dt><span class="term">fopt :</span>
      <dd><p class="para">a double, the value of the function at x.</p></dd></dt>
   <dt><span class="term">exitflag :</span>
      <dd><p class="para">The exit status. See below for details.</p></dd></dt>
   <dt><span class="term">output :</span>
      <dd><p class="para">The structure consist of statistics about the optimization. See below for details.</p></dd></dt></dl></div>

<div class="refsection"><h3 class="title">Description</h3>
   <p class="para">Search the minimum of a constrained linear quadratic optimization problem specified by :</p>
   <p class="para"><span><img src='./_LaTeX_intqpipopt.xml_1.png' style='position:relative;top:52px;width:277px;height:112px'/></span></p>
   <p class="para">The routine calls Bonmin for solving the quadratic problem, Bonmin is a library written in C++.</p>
   <p class="para">The exitflag allows to know the status of the optimization which is given back by Bonmin.
<ul class="itemizedlist"><li>exitflag=0 : Optimal Solution Found.</li>
<li>exitflag=1 : InFeasible Solution.</li>
<li>exitflag=2 : Output is Continuous Unbounded.</li>
<li>exitflag=3 : Limit Exceeded.</li>
<li>exitflag=4 : User Interrupt.</li>
<li>exitflag=5 : MINLP Error.</li></ul></p>
   <p class="para">For more details on exitflag see the Bonmin page, go to http://www.coin-or.org/Bonmin</p>
   <p class="para">The output data structure contains detailed informations about the optimization process.
It has type &#0034;struct&#0034; and contains the following fields.
<ul class="itemizedlist"><li>output.constrviolation: The max-norm of the constraint violation.</li></ul></p>
   <p class="para"></p></div>

<div class="refsection"><h3 class="title">Examples</h3>
   <div class="programlisting"><table border="0" width="100%"><tr><td width="98%"><pre class="scilabcode"><span class="scilabid">H</span> <span class="scilaboperator">=</span> <span class="scilabopenclose">[</span><span class="scilabnumber">1</span> <span class="scilaboperator">-</span><span class="scilabnumber">1</span><span class="scilabdefault">;</span> <span class="scilaboperator">-</span><span class="scilabnumber">1</span> <span class="scilabnumber">2</span><span class="scilabopenclose">]</span><span class="scilabdefault">;</span>
<span class="scilabid">f</span> <span class="scilaboperator">=</span> <span class="scilabopenclose">[</span><span class="scilaboperator">-</span><span class="scilabnumber">2</span><span class="scilabdefault">;</span> <span class="scilaboperator">-</span><span class="scilabnumber">6</span><span class="scilabopenclose">]</span><span class="scilabdefault">;</span>
<span class="scilabid">A</span> <span class="scilaboperator">=</span> <span class="scilabopenclose">[</span><span class="scilabnumber">1</span> <span class="scilabnumber">1</span><span class="scilabdefault">;</span> <span class="scilaboperator">-</span><span class="scilabnumber">1</span> <span class="scilabnumber">2</span><span class="scilabdefault">;</span> <span class="scilabnumber">2</span> <span class="scilabnumber">1</span><span class="scilabopenclose">]</span><span class="scilabdefault">;</span>
<span class="scilabid">b</span> <span class="scilaboperator">=</span> <span class="scilabopenclose">[</span><span class="scilabnumber">2</span><span class="scilabdefault">;</span> <span class="scilabnumber">2</span><span class="scilabdefault">;</span> <span class="scilabnumber">3</span><span class="scilabopenclose">]</span><span class="scilabdefault">;</span>
<span class="scilabid">lb</span><span class="scilaboperator">=</span><span class="scilabopenclose">[</span><span class="scilabnumber">0</span><span class="scilabdefault">,</span><span class="scilabnumber">0</span><span class="scilabopenclose">]</span><span class="scilabdefault">;</span>
<span class="scilabid">ub</span><span class="scilaboperator">=</span><span class="scilabopenclose">[</span><span class="scilabconstants">%inf</span><span class="scilabdefault">,</span> <span class="scilabconstants">%inf</span><span class="scilabopenclose">]</span><span class="scilabdefault">;</span>
<span class="scilabid">intcon</span> <span class="scilaboperator">=</span> <span class="scilabopenclose">[</span><span class="scilabnumber">1</span> <span class="scilabnumber">2</span><span class="scilabopenclose">]</span><span class="scilabdefault">;</span>
<span class="scilabopenclose">[</span><span class="scilabid">xopt</span><span class="scilabdefault">,</span><span class="scilabid">fopt</span><span class="scilabdefault">,</span><span class="scilabid">status</span><span class="scilabdefault">,</span><span class="scilabid">output</span><span class="scilabopenclose">]</span><span class="scilaboperator">=</span><span class="scilabid">intqpipopt</span><span class="scilabopenclose">(</span><span class="scilabid">H</span><span class="scilabdefault">,</span><span class="scilabid">f</span><span class="scilabdefault">,</span><span class="scilabid">intcon</span><span class="scilabdefault">,</span><span class="scilabid">A</span><span class="scilabdefault">,</span><span class="scilabid">b</span><span class="scilabdefault">,</span><span class="scilabopenclose">[</span><span class="scilabopenclose">]</span><span class="scilabdefault">,</span><span class="scilabopenclose">[</span><span class="scilabopenclose">]</span><span class="scilabdefault">,</span><span class="scilabid">lb</span><span class="scilabdefault">,</span><span class="scilabid">ub</span><span class="scilabopenclose">)</span></pre></td><td valign="top"><a href="scilab://scilab.execexample/"><img src="ScilabExecute.png" border="0"/></a></td><td valign="top"><a href="scilab://scilab.editexample/"><img src="ScilabEdit.png" border="0"/></a></td><td></td></tr></table></div></div>

<div class="refsection"><h3 class="title">Examples</h3>
   <div class="programlisting"><table border="0" width="100%"><tr><td width="98%"><pre class="scilabcode"><span class="scilabcomment">//Find x in R^6 such that:</span>
<span class="scilabid">Aeq</span><span class="scilaboperator">=</span> <span class="scilabopenclose">[</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilaboperator">-</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilabnumber">0</span><span class="scilabdefault">,</span><span class="scilabnumber">3</span><span class="scilabdefault">,</span><span class="scilabnumber">1</span><span class="scilabdefault">;</span>
<span class="scilaboperator">-</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilabnumber">0</span><span class="scilabdefault">,</span><span class="scilaboperator">-</span><span class="scilabnumber">3</span><span class="scilabdefault">,</span><span class="scilaboperator">-</span><span class="scilabnumber">4</span><span class="scilabdefault">,</span><span class="scilabnumber">5</span><span class="scilabdefault">,</span><span class="scilabnumber">6</span><span class="scilabdefault">;</span>
<span class="scilabnumber">2</span><span class="scilabdefault">,</span><span class="scilabnumber">5</span><span class="scilabdefault">,</span><span class="scilabnumber">3</span><span class="scilabdefault">,</span><span class="scilabnumber">0</span><span class="scilabdefault">,</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilabnumber">0</span><span class="scilabopenclose">]</span><span class="scilabdefault">;</span>
<span class="scilabid">beq</span><span class="scilaboperator">=</span><span class="scilabopenclose">[</span><span class="scilabnumber">1</span><span class="scilabdefault">;</span> <span class="scilabnumber">2</span><span class="scilabdefault">;</span> <span class="scilabnumber">3</span><span class="scilabopenclose">]</span><span class="scilabdefault">;</span>
<span class="scilabid">A</span><span class="scilaboperator">=</span> <span class="scilabopenclose">[</span><span class="scilabnumber">0</span><span class="scilabdefault">,</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilabnumber">0</span><span class="scilabdefault">,</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilabnumber">2</span><span class="scilabdefault">,</span><span class="scilaboperator">-</span><span class="scilabnumber">1</span><span class="scilabdefault">;</span>
<span class="scilaboperator">-</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilabnumber">0</span><span class="scilabdefault">,</span><span class="scilabnumber">2</span><span class="scilabdefault">,</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilabnumber">0</span><span class="scilabopenclose">]</span><span class="scilabdefault">;</span>
<span class="scilabid">b</span> <span class="scilaboperator">=</span> <span class="scilabopenclose">[</span><span class="scilaboperator">-</span><span class="scilabnumber">1</span><span class="scilabdefault">;</span> <span class="scilabnumber">2.5</span><span class="scilabopenclose">]</span><span class="scilabdefault">;</span>
<span class="scilabid">lb</span><span class="scilaboperator">=</span><span class="scilabopenclose">[</span><span class="scilaboperator">-</span><span class="scilabnumber">1000</span><span class="scilabdefault">;</span> <span class="scilaboperator">-</span><span class="scilabnumber">10000</span><span class="scilabdefault">;</span> <span class="scilabnumber">0</span><span class="scilabdefault">;</span> <span class="scilaboperator">-</span><span class="scilabnumber">1000</span><span class="scilabdefault">;</span> <span class="scilaboperator">-</span><span class="scilabnumber">1000</span><span class="scilabdefault">;</span> <span class="scilaboperator">-</span><span class="scilabnumber">1000</span><span class="scilabopenclose">]</span><span class="scilabdefault">;</span>
<span class="scilabid">ub</span><span class="scilaboperator">=</span><span class="scilabopenclose">[</span><span class="scilabnumber">10000</span><span class="scilabdefault">;</span> <span class="scilabnumber">100</span><span class="scilabdefault">;</span> <span class="scilabnumber">1.5</span><span class="scilabdefault">;</span> <span class="scilabnumber">100</span><span class="scilabdefault">;</span> <span class="scilabnumber">100</span><span class="scilabdefault">;</span> <span class="scilabnumber">1000</span><span class="scilabopenclose">]</span><span class="scilabdefault">;</span>
<span class="scilabid">x0</span> <span class="scilaboperator">=</span> <a class="scilabmacro" href="scilab://repmat">repmat</a><span class="scilabopenclose">(</span><span class="scilabnumber">0</span><span class="scilabdefault">,</span><span class="scilabnumber">6</span><span class="scilabdefault">,</span><span class="scilabnumber">1</span><span class="scilabopenclose">)</span><span class="scilabdefault">;</span>
<span class="scilabid">param</span> <span class="scilaboperator">=</span> <a class="scilabcommand" href="scilab://list">list</a><span class="scilabopenclose">(</span><span class="scilabstring">&#0034;</span><span class="scilabstring">MaxIter</span><span class="scilabstring">&#0034;</span><span class="scilabdefault">,</span> <span class="scilabnumber">300</span><span class="scilabdefault">,</span> <span class="scilabstring">&#0034;</span><span class="scilabstring">CpuTime</span><span class="scilabstring">&#0034;</span><span class="scilabdefault">,</span> <span class="scilabnumber">100</span><span class="scilabopenclose">)</span><span class="scilabdefault">;</span>
<span class="scilabcomment">//and minimize 0.5*x</span><span class="scilabcomment">&#0039;</span><span class="scilabcomment">*H*x + f</span><span class="scilabcomment">&#0039;</span><span class="scilabcomment">*x with</span>
<span class="scilabid">f</span><span class="scilaboperator">=</span><span class="scilabopenclose">[</span><span class="scilabnumber">1</span><span class="scilabdefault">;</span> <span class="scilabnumber">2</span><span class="scilabdefault">;</span> <span class="scilabnumber">3</span><span class="scilabdefault">;</span> <span class="scilabnumber">4</span><span class="scilabdefault">;</span> <span class="scilabnumber">5</span><span class="scilabdefault">;</span> <span class="scilabnumber">6</span><span class="scilabopenclose">]</span><span class="scilabdefault">;</span> <span class="scilabid">H</span><span class="scilaboperator">=</span><a class="scilabcommand" href="scilab://eye">eye</a><span class="scilabopenclose">(</span><span class="scilabnumber">6</span><span class="scilabdefault">,</span><span class="scilabnumber">6</span><span class="scilabopenclose">)</span><span class="scilabdefault">;</span>
<span class="scilabid">intcon</span> <span class="scilaboperator">=</span> <span class="scilabopenclose">[</span><span class="scilabnumber">2</span> <span class="scilabnumber">4</span><span class="scilabopenclose">]</span><span class="scilabdefault">;</span>
<span class="scilabopenclose">[</span><span class="scilabid">xopt</span><span class="scilabdefault">,</span><span class="scilabid">fopt</span><span class="scilabdefault">,</span><span class="scilabid">exitflag</span><span class="scilabdefault">,</span><span class="scilabid">output</span><span class="scilabopenclose">]</span><span class="scilaboperator">=</span><span class="scilabid">intqpipopt</span><span class="scilabopenclose">(</span><span class="scilabid">H</span><span class="scilabdefault">,</span><span class="scilabid">f</span><span class="scilabdefault">,</span><span class="scilabid">intcon</span><span class="scilabdefault">,</span><span class="scilabid">A</span><span class="scilabdefault">,</span><span class="scilabid">b</span><span class="scilabdefault">,</span><span class="scilabid">Aeq</span><span class="scilabdefault">,</span><span class="scilabid">beq</span><span class="scilabdefault">,</span><span class="scilabid">lb</span><span class="scilabdefault">,</span><span class="scilabid">ub</span><span class="scilabdefault">,</span><span class="scilabid">x0</span><span class="scilabdefault">,</span><span class="scilabid">param</span><span class="scilabopenclose">)</span></pre></td><td valign="top"><a href="scilab://scilab.execexample/"><img src="ScilabExecute.png" border="0"/></a></td><td valign="top"><a href="scilab://scilab.editexample/"><img src="ScilabEdit.png" border="0"/></a></td><td></td></tr></table></div></div>

<div class="refsection"><h3 class="title">Authors</h3>
   <ul class="itemizedlist"><li class="member">Akshay Miterani and Pranav Deshpande</li></ul></div>
    <br />

    <div class="manualnavbar">
    <table width="100%">
    <tr><td colspan="3" class="next"><a href="http://bugzilla.scilab.org/enter_bug.cgi?product=Scilab%20software&component=Documentation%20pages" class="ulink">Report an issue</a></td></tr>
<tr>
      <td width="30%">
    	<span class="previous"><a href="intfminunc.html">&lt;&lt; intfminunc</a></span>

      </td>
      <td width="40%" class="center">
      	<span class="top"><a href="section_2f30ec7805b02b8760d8add3187208be.html">FOSSEE Optimization Toolbox</a></span>

      </td>
      <td width="30%" class="next">
      	
      </td>
    </tr></table>
      <hr />
    </div>
  </body>
</html>