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
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
|
<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
<html>
<!-- Additional documentation for the optim package for Octave.
Copyright (C) Olaf Till <i7tiol@t-online.de>
You can redistribute this documentation and/or modify it under the terms
of the GNU General Public License as published by the Free Software
Foundation; either version 3 of the License, or (at your option) any
later version.
This documentation is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General
Public License for more details.
You should have received a copy of the GNU General Public License along
with this documentation; if not, see <http://www.gnu.org/licenses/>. -->
<!-- Created by GNU Texinfo 6.5, http://www.gnu.org/software/texinfo/ -->
<head>
<meta http-equiv="Content-Type" content="text/html; charset=utf-8">
<title>fmincon (optim_doc)</title>
<meta name="description" content="fmincon (optim_doc)">
<meta name="keywords" content="fmincon (optim_doc)">
<meta name="resource-type" content="document">
<meta name="distribution" content="global">
<meta name="Generator" content="makeinfo">
<link href="index.html#Top" rel="start" title="Top">
<link href="Function-index.html#Function-index" rel="index" title="Function index">
<link href="Compatibility-functions.html#Compatibility-functions" rel="up" title="Compatibility functions">
<link href="Common-frontend-options.html#Common-frontend-options" rel="next" title="Common frontend options">
<link href="nlinfit.html#nlinfit" rel="prev" title="nlinfit">
<style type="text/css">
<!--
a.summary-letter {text-decoration: none}
blockquote.indentedblock {margin-right: 0em}
blockquote.smallindentedblock {margin-right: 0em; font-size: smaller}
blockquote.smallquotation {font-size: smaller}
div.display {margin-left: 3.2em}
div.example {margin-left: 3.2em}
div.lisp {margin-left: 3.2em}
div.smalldisplay {margin-left: 3.2em}
div.smallexample {margin-left: 3.2em}
div.smalllisp {margin-left: 3.2em}
kbd {font-style: oblique}
pre.display {font-family: inherit}
pre.format {font-family: inherit}
pre.menu-comment {font-family: serif}
pre.menu-preformatted {font-family: serif}
pre.smalldisplay {font-family: inherit; font-size: smaller}
pre.smallexample {font-size: smaller}
pre.smallformat {font-family: inherit; font-size: smaller}
pre.smalllisp {font-size: smaller}
span.nolinebreak {white-space: nowrap}
span.roman {font-family: initial; font-weight: normal}
span.sansserif {font-family: sans-serif; font-weight: normal}
ul.no-bullet {list-style: none}
-->
</style>
</head>
<body lang="en">
<a name="fmincon"></a>
<div class="header">
<p>
Previous: <a href="nlinfit.html#nlinfit" accesskey="p" rel="prev">nlinfit</a>, Up: <a href="Compatibility-functions.html#Compatibility-functions" accesskey="u" rel="up">Compatibility functions</a> [<a href="Function-index.html#Function-index" title="Index" rel="index">Index</a>]</p>
</div>
<hr>
<a name="Non_002dlinear-scalar-optimization"></a>
<h3 class="section">7.6 Non-linear scalar optimization</h3>
<a name="index-fmincon-8"></a>
<a name="XREFfmincon"></a><dl>
<dt><a name="index-fmincon"></a>Function File: <em></em> <strong>fmincon</strong> <em>(<var>objf</var>, <var>x0</var>)</em></dt>
<dt><a name="index-fmincon-1"></a>Function File: <em></em> <strong>fmincon</strong> <em>(<var>objf</var>, <var>x0</var>, <var>A</var>, <var>b</var>)</em></dt>
<dt><a name="index-fmincon-2"></a>Function File: <em></em> <strong>fmincon</strong> <em>(<var>objf</var>, <var>x0</var>, <var>A</var>, <var>b</var>, <var>Aeq</var>, <var>beq</var>)</em></dt>
<dt><a name="index-fmincon-3"></a>Function File: <em></em> <strong>fmincon</strong> <em>(<var>objf</var>, <var>x0</var>, <var>A</var>, <var>b</var>, <var>Aeq</var>, <var>beq</var>, <var>lb</var>, <var>ub</var>)</em></dt>
<dt><a name="index-fmincon-4"></a>Function File: <em></em> <strong>fmincon</strong> <em>(<var>objf</var>, <var>x0</var>, <var>A</var>, <var>b</var>, <var>Aeq</var>, <var>beq</var>, <var>lb</var>, <var>ub</var>, <var>nonlcon</var>)</em></dt>
<dt><a name="index-fmincon-5"></a>Function File: <em></em> <strong>fmincon</strong> <em>(<var>objf</var>, <var>x0</var>, <var>A</var>, <var>b</var>, <var>Aeq</var>, <var>beq</var>, <var>lb</var>, <var>ub</var>, <var>nonlcon</var>, <var>options</var>)</em></dt>
<dt><a name="index-fmincon-6"></a>Function File: <em></em> <strong>fmincon</strong> <em>(<var>problem</var>)</em></dt>
<dt><a name="index-fmincon-7"></a>Function File: <em>[<var>x</var>, <var>fval</var>, <var>cvg</var>, <var>outp</var>] =</em> <strong>fmincon</strong> <em>(…)</em></dt>
<dd><p>Compatibility frontend for nonlinear minimization of a scalar
objective function.
</p>
<p>This function is for Matlab compatibility and provides a subset of
the functionality of <code>nonlin_min</code>.
</p>
<p><var>objf</var>: objective function. It gets the real parameters as
argument.
</p>
<p><var>x0</var>: real vector or array of initial parameters.
</p>
<p><var>A</var>, <var>b</var>: Inequality constraints of the parameters <code>p</code>
with <code>A * p - b <= 0</code>.
</p>
<p><var>Aeq</var>, <var>beq</var>: Equality constraints of the parameters <code>p</code>
with <code>A * p - b = 0</code>.
</p>
<p><var>lb</var>, <var>ub</var>: Bounds of the parameters <code>p</code> with <code>lb
<= p <= ub</code>. Vectors or arrays. If the number of elements is
smaller than the number of parameters, as many bounds as present
are applied, starting with the first parameter. This is for
compatibility with Matlab.
</p>
<p><var>nonlcon</var>: Nonlinear constraints. Function returning the
current values of nonlinear inequality constraints (constrained to
<code><= 0</code>) in the first output and the current values of nonlinear
equality constraints in the second output.
</p>
<p><var>options</var>: structure whose fields stand for optional settings
referred to below. The fields can be set by <code>optimset()</code>.
</p>
<p>An argument can be set to <code>[]</code> to indicate that its value is
not set.
</p>
<p><code>fmincon</code> may also be called with a single structure
argument with the fields <code>objective</code>, <code>x0</code>, <code>Aineq</code>,
<code>bineq</code>, <code>Aeq</code>, <code>beq</code>, <code>lb</code>, <code>ub</code>,
<code>nonlcon</code> and <code>options</code>, resembling
the separate input arguments above. Additionally,
the structure must have the field <code>solver</code>, set to
<code>"fmincon"</code>.
</p>
<p>The returned values are the final parameters <var>x</var>, the final
value of the objective function <var>fval</var>, an integer <var>cvg</var>
indicating if and how optimization succeeded or failed, and a
structure <var>outp</var> with additional information, curently with
possible fields: <code>iterations</code>, the number of iterations,
<code>funcCount</code>, the number of objective function calls (indirect
calls by gradient function not counted), <code>constrviolation</code>,
the maximum of the constraint violations. The backend may define
additional fields. <var>cvg</var> is greater than zero for success and
less than or equal to zero for failure; its possible values depend
on the used backend and currently can be <code>0</code> (maximum number
of iterations exceeded), <code>1</code> (success without further
specification of criteria), <code>2</code> (parameter change less than
specified precision in two consecutive iterations), <code>3</code>
(improvement in objective function less than specified), <code>-1</code>
(algorithm aborted by a user function), or <code>-4</code> (algorithm got
stuck).
</p>
<a name="Options_003a"></a>
<h4 class="subsubheading">Options:</h4>
<dl compact="compact">
<dt><code>Algorithm</code></dt>
<dd><p><code>interior-point</code>, <code>sqp</code>, and <code>sqp-legacy</code> are
mapped to optims <code>lm_feasible</code> algorithm (the default) to
satisfy constraints throughout the optimization. <code>active-set</code>
is mapped to <code>octave_sqp</code>, which may perform better if
constraints only need to be satisfied for the result. Other
algorithms are available with <code>nonlin_min</code>.
</p>
</dd>
<dt><code>OutputFcn</code></dt>
<dd><p>Similar to the setting <code>user_interaction</code> — see
<code>optim_doc()</code>. Differently, <code>OutputFcn</code> returns only one
output argument, the <var>stop</var> flag.
</p>
</dd>
<dt><code>GradObj</code></dt>
<dd><p>If set to <code>"on"</code>, <var>objf</var> must return the gradient of the
objective function as a second output. The default is <code>"off"</code>.
</p>
</dd>
<dt><code>GradConstr</code></dt>
<dd><p>If set to <code>"on"</code>, <var>nonlcon</var> must return the Jacobians of
the inequality- and equality-constraints as third and fourth
output, respectively.
</p>
</dd>
<dt><code>HessianFcn</code></dt>
<dd><p>If set to <code>"objective"</code>, <var>objf</var> must not only return the
gradient as the second, but also the Hessian as the third output.
</p>
</dd>
<dt><code>Display, FinDiffRelStep, FinDiffType, TypicalX, MaxIter, TolFun, TolX,</code></dt>
<dd><p>See documentation of these options in <code>optim_doc()</code>.
</p>
</dd>
</dl>
<p>For description of individual backends, type
<code>optim_doc ("scalar optimization")</code> and choose the backend in
the menu.
</p>
</dd></dl>
<hr>
<div class="header">
<p>
Previous: <a href="nlinfit.html#nlinfit" accesskey="p" rel="prev">nlinfit</a>, Up: <a href="Compatibility-functions.html#Compatibility-functions" accesskey="u" rel="up">Compatibility functions</a> [<a href="Function-index.html#Function-index" title="Index" rel="index">Index</a>]</p>
</div>
</body>
</html>
|
