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
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
|
<?xml version="1.0" encoding="UTF-8"?>
<!--
*
* This help file was generated from intqpipopt.sci using help_from_sci().
*
-->
<refentry version="5.0-subset Scilab" xml:id="intqpipopt" 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:ns3="http://www.w3.org/1999/xhtml"
xmlns:mml="http://www.w3.org/1998/Math/MathML"
xmlns:scilab="http://www.scilab.org"
xmlns:db="http://docbook.org/ns/docbook">
<refnamediv>
<refname>intqpipopt</refname>
<refpurpose>Solves a linear quadratic problem.</refpurpose>
</refnamediv>
<refsynopsisdiv>
<title>Calling Sequence</title>
<synopsis>
xopt = intqpipopt(H,f)
xopt = intqpipopt(H,f,intcon)
xopt = intqpipopt(H,f,intcon,A,b)
xopt = intqpipopt(H,f,intcon,A,b,Aeq,beq)
xopt = intqpipopt(H,f,intcon,A,b,Aeq,beq,lb,ub)
xopt = intqpipopt(H,f,intcon,A,b,Aeq,beq,lb,ub,x0)
xopt = intqpipopt(H,f,intcon,A,b,Aeq,beq,lb,ub,x0,options)
xopt = intqpipopt(H,f,intcon,A,b,Aeq,beq,lb,ub,x0,options,"file_path")
[xopt,fopt,exitflag,output] = intqpipopt( ... )
</synopsis>
</refsynopsisdiv>
<refsection>
<title>Parameters</title>
<variablelist>
<varlistentry><term>H :</term>
<listitem><para> a symmetric matrix of double, represents coefficients of quadratic in the quadratic problem.</para></listitem></varlistentry>
<varlistentry><term>f :</term>
<listitem><para> a vector of double, represents coefficients of linear in the quadratic problem</para></listitem></varlistentry>
<varlistentry><term>intcon :</term>
<listitem><para> a vector of integers, represents which variables are constrained to be integers</para></listitem></varlistentry>
<varlistentry><term>A :</term>
<listitem><para> a matrix of double, represents the linear coefficients in the inequality constraints A⋅x ≤ b.</para></listitem></varlistentry>
<varlistentry><term>b :</term>
<listitem><para> a vector of double, represents the linear coefficients in the inequality constraints A⋅x ≤ b.</para></listitem></varlistentry>
<varlistentry><term>Aeq :</term>
<listitem><para> a matrix of double, represents the linear coefficients in the equality constraints Aeq⋅x = beq.</para></listitem></varlistentry>
<varlistentry><term>beq :</term>
<listitem><para> a vector of double, represents the linear coefficients in the equality constraints Aeq⋅x = beq.</para></listitem></varlistentry>
<varlistentry><term>lb :</term>
<listitem><para> a vector of double, contains lower bounds of the variables.</para></listitem></varlistentry>
<varlistentry><term>ub :</term>
<listitem><para> a vector of double, contains upper bounds of the variables.</para></listitem></varlistentry>
<varlistentry><term>x0 :</term>
<listitem><para> a vector of double, contains initial guess of variables.</para></listitem></varlistentry>
<varlistentry><term>options :</term>
<listitem><para> a list containing the parameters to be set.</para></listitem></varlistentry>
<varlistentry><term>file_path :</term>
<listitem><para> path to bonmin opt file if used.</para></listitem></varlistentry>
<varlistentry><term>xopt :</term>
<listitem><para> a vector of double, the computed solution of the optimization problem.</para></listitem></varlistentry>
<varlistentry><term>fopt :</term>
<listitem><para> a double, the value of the function at x.</para></listitem></varlistentry>
<varlistentry><term>exitflag :</term>
<listitem><para> The exit status. See below for details.</para></listitem></varlistentry>
<varlistentry><term>output :</term>
<listitem><para> The structure consist of statistics about the optimization. See below for details.</para></listitem></varlistentry>
</variablelist>
</refsection>
<refsection>
<title>Description</title>
<para>
Search the minimum of a constrained linear quadratic optimization problem specified by :
</para>
<para>
<latex>
\begin{eqnarray}
&\mbox{min}_{x}
& 1/2⋅x^T⋅H⋅x + f^T⋅x \\
& \text{subject to} & A⋅x \leq b \\
& & Aeq⋅x = beq \\
& & lb \leq x \leq ub \\
& & x_i \in \!\, \mathbb{Z}, i \in \!\, intcon\\
\end{eqnarray}
</latex>
</para>
<para>
The routine calls Bonmin for solving the quadratic problem, Bonmin is a library written in C++.
</para>
<para>
The exitflag allows to know the status of the optimization which is given back by Bonmin.
<itemizedlist>
<listitem>exitflag=0 : Optimal Solution Found. </listitem>
<listitem>exitflag=1 : InFeasible Solution.</listitem>
<listitem>exitflag=2 : Output is Continuous Unbounded.</listitem>
<listitem>exitflag=3 : Limit Exceeded.</listitem>
<listitem>exitflag=4 : User Interrupt.</listitem>
<listitem>exitflag=5 : MINLP Error.</listitem>
</itemizedlist>
</para>
<para>
For more details on exitflag see the Bonmin page, go to http://www.coin-or.org/Bonmin
</para>
<para>
The output data structure contains detailed informations about the optimization process.
It has type "struct" and contains the following fields.
<itemizedlist>
<listitem>output.constrviolation: The max-norm of the constraint violation.</listitem>
</itemizedlist>
</para>
<para>
</para>
</refsection>
<refsection>
<title>Examples</title>
<programlisting role="example"><![CDATA[
H = [1 -1; -1 2];
f = [-2; -6];
A = [1 1; -1 2; 2 1];
b = [2; 2; 3];
lb=[0,0];
ub=[%inf, %inf];
intcon = [1 2];
[xopt,fopt,status,output]=intqpipopt(H,f,intcon,A,b,[],[],lb,ub)
]]></programlisting>
</refsection>
<refsection>
<title>Examples</title>
<programlisting role="example"><![CDATA[
//Find x in R^6 such that:
Aeq= [1,-1,1,0,3,1;
-1,0,-3,-4,5,6;
2,5,3,0,1,0];
beq=[1; 2; 3];
A= [0,1,0,1,2,-1;
-1,0,2,1,1,0];
b = [-1; 2.5];
lb=[-1000; -10000; 0; -1000; -1000; -1000];
ub=[10000; 100; 1.5; 100; 100; 1000];
x0 = repmat(0,6,1);
param = list("MaxIter", 300, "CpuTime", 100);
//and minimize 0.5*x'*H*x + f'*x with
f=[1; 2; 3; 4; 5; 6]; H=eye(6,6);
intcon = [2 4];
[xopt,fopt,exitflag,output]=intqpipopt(H,f,intcon,A,b,Aeq,beq,lb,ub,x0,param)
]]></programlisting>
</refsection>
<refsection>
<title>Authors</title>
<simplelist type="vert">
<member>Akshay Miterani and Pranav Deshpande</member>
</simplelist>
</refsection>
</refentry>
|
