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
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
|
<?xml version="1.0" encoding="UTF-8"?>
<!--
*
* This help file was generated from intfminbnd.sci using help_from_sci().
*
-->
<refentry version="5.0-subset Scilab" xml:id="intfminbnd" 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>intfminbnd</refname>
<refpurpose>Solves a multi-variable optimization problem on a bounded interval</refpurpose>
</refnamediv>
<refsynopsisdiv>
<title>Calling Sequence</title>
<synopsis>
xopt = intfminbnd(f,intcon,x1,x2)
xopt = intfminbnd(f,intcon,x1,x2,options)
[xopt,fopt] = intfminbnd(.....)
[xopt,fopt,exitflag]= intfminbnd(.....)
[xopt,fopt,exitflag,output]=intfminbnd(.....)
[xopt,fopt,exitflag,gradient,hessian]=intfminbnd(.....)
</synopsis>
</refsynopsisdiv>
<refsection>
<title>Parameters</title>
<variablelist>
<varlistentry><term>f :</term>
<listitem><para> a function, representing the objective function of the problem</para></listitem></varlistentry>
<varlistentry><term>x1 :</term>
<listitem><para> a vector, containing the lower bound of the variables.</para></listitem></varlistentry>
<varlistentry><term>x2 :</term>
<listitem><para> a vector, containing the upper bound of the variables.</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>options :</term>
<listitem><para> a list, containing the option for user to specify. See below for details.</para></listitem></varlistentry>
<varlistentry><term>xopt :</term>
<listitem><para> a vector of doubles, containing the the computed solution of the optimization problem.</para></listitem></varlistentry>
<varlistentry><term>fopt :</term>
<listitem><para> a scalar of double, containing the the function value at x.</para></listitem></varlistentry>
<varlistentry><term>exitflag :</term>
<listitem><para> a scalar of integer, containing the flag which denotes the reason for termination of algorithm. See below for details.</para></listitem></varlistentry>
<varlistentry><term>gradient :</term>
<listitem><para> a vector of doubles, containing the Objective's gradient of the solution.</para></listitem></varlistentry>
<varlistentry><term>hessian :</term>
<listitem><para> a matrix of doubles, containing the Objective's hessian of the solution.</para></listitem></varlistentry>
</variablelist>
</refsection>
<refsection>
<title>Description</title>
<para>
Search the minimum of a multi-variable function on bounded interval specified by :
Find the minimum of f(x) such that
</para>
<para>
<latex>
\begin{eqnarray}
&\mbox{min}_{x}
& f(x)\\
& \text{subject to} & x1 \ < x \ < x2 \\
\end{eqnarray}
</latex>
</para>
<para>
The routine calls Bonmin for solving the Bounded Optimization problem, Bonmin is a library written in C++.
</para>
<para>
The options allows the user to set various parameters of the Optimization problem.
It should be defined as type "list" and contains the following fields.
<itemizedlist>
<listitem>Syntax : options= list("IntegerTolerance", [---], "MaxNodes",[---], "MaxIter", [---], "AllowableGap",[---] "CpuTime", [---],"gradobj", "off", "hessian", "off" );</listitem>
<listitem>IntegerTolerance : a Scalar, a number with that value of an integer is considered integer..</listitem>
<listitem>MaxNodes : a Scalar, containing the Maximum Number of Nodes that the solver should search.</listitem>
<listitem>CpuTime : a Scalar, containing the Maximum amount of CPU Time that the solver should take.</listitem>
<listitem>AllowableGap : a Scalar, to stop the tree search when the gap between the objective value of the best known solution is reached.</listitem>
<listitem>MaxIter : a Scalar, containing the Maximum Number of Iteration that the solver should take.</listitem>
<listitem>gradobj : a string, to turn on or off the user supplied objective gradient.</listitem>
<listitem>hessian : a Scalar, to turn on or off the user supplied objective hessian.</listitem>
<listitem>Default Values : options = list('integertolerance',1d-06,'maxnodes',2147483647,'cputime',1d10,'allowablegap',0,'maxiter',2147483647,'gradobj',"off",'hessian',"off")</listitem>
</itemizedlist>
</para>
<para>
The exitflag allows to know the status of the optimization which is given back by Ipopt.
<itemizedlist>
<listitem>exitflag=0 : Optimal Solution Found </listitem>
<listitem>exitflag=1 : Maximum Number of Iterations Exceeded. Output may not be optimal.</listitem>
<listitem>exitflag=2 : Maximum CPU Time exceeded. Output may not be optimal.</listitem>
<listitem>exitflag=3 : Stop at Tiny Step.</listitem>
<listitem>exitflag=4 : Solved To Acceptable Level.</listitem>
<listitem>exitflag=5 : Converged to a point of local infeasibility.</listitem>
</itemizedlist>
</para>
<para>
For more details on exitflag see the Bonmin documentation, go to http://www.coin-or.org/Bonmin
</para>
<para>
</para>
</refsection>
<refsection>
<title>Examples</title>
<programlisting role="example"><![CDATA[
//Find x in R^6 such that it minimizes:
//f(x)= sin(x1) + sin(x2) + sin(x3) + sin(x4) + sin(x5) + sin(x6)
//-2 <= x1,x2,x3,x4,x5,x6 <= 2
//Objective function to be minimised
function y=f(x)
y=0
for i =1:6
y=y+sin(x(i));
end
endfunction
//Variable bounds
x1 = [-2, -2, -2, -2, -2, -2];
x2 = [2, 2, 2, 2, 2, 2];
intcon = [2 3 4]
//Options
options=list("MaxIter",[1500],"CpuTime", [100])
[x,fval] =intfminbnd(f ,intcon, x1, x2, options)
// Press ENTER to continue
]]></programlisting>
</refsection>
<refsection>
<title>Examples</title>
<programlisting role="example"><![CDATA[
//Find x in R such that it minimizes:
//f(x)= 1/x^2
//0 <= x <= 1000
//Objective function to be minimised
function y=f(x)
y=1/x^2;
endfunction
//Variable bounds
x1 = [0];
x2 = [1000];
intcon = [1];
[x,fval,exitflag,output,lambda] =intfminbnd(f,intcon , x1, x2)
// Press ENTER to continue
]]></programlisting>
</refsection>
<refsection>
<title>Examples</title>
<programlisting role="example"><![CDATA[
//The below problem is an unbounded problem:
//Find x in R^2 such that it minimizes:
//f(x)= -[(x1-1)^2 + (x2-1)^2]
//-inf <= x1,x2 <= inf
//Objective function to be minimised
function y=f(x)
y=-((x(1)-1)^2+(x(2)-1)^2);
endfunction
//Variable bounds
x1 = [-%inf , -%inf];
x2 = [ %inf , %inf];
//Options
options=list("MaxIter",[1500],"CpuTime", [100])
[x,fval,exitflag,output,lambda] =intfminbnd(f,intcon, x1, x2, options)
]]></programlisting>
</refsection>
<refsection>
<title>Authors</title>
<simplelist type="vert">
<member>Harpreet Singh</member>
</simplelist>
</refsection>
</refentry>
|
