Mercurial > octave-nkf
annotate doc/interpreter/optim.txi @ 19630:0e1f5a750d00
maint: Periodic merge of gui-release to default.
| author | John W. Eaton <jwe@octave.org> |
|---|---|
| date | Tue, 20 Jan 2015 10:24:46 -0500 |
| parents | c9113e28fae8 446c46af4b42 |
| children | 4197fc428c7d |
| rev | line source |
|---|---|
|
17744
d63878346099
maint: Update copyright notices for release.
John W. Eaton <jwe@octave.org>
parents:
17152
diff
changeset
|
1 @c Copyright (C) 1996-2013 John W. Eaton |
| 7018 | 2 @c |
| 3 @c This file is part of Octave. | |
| 4 @c | |
| 5 @c Octave is free software; you can redistribute it and/or modify it | |
| 6 @c under the terms of the GNU General Public License as published by the | |
| 7 @c Free Software Foundation; either version 3 of the License, or (at | |
| 8 @c your option) any later version. | |
|
19627
446c46af4b42
strip trailing whitespace from most source files
John W. Eaton <jwe@octave.org>
parents:
17744
diff
changeset
|
9 @c |
| 7018 | 10 @c Octave is distributed in the hope that it will be useful, but WITHOUT |
| 11 @c ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or | |
| 12 @c FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License | |
| 13 @c for more details. | |
|
19627
446c46af4b42
strip trailing whitespace from most source files
John W. Eaton <jwe@octave.org>
parents:
17744
diff
changeset
|
14 @c |
| 7018 | 15 @c You should have received a copy of the GNU General Public License |
| 16 @c along with Octave; see the file COPYING. If not, see | |
| 17 @c <http://www.gnu.org/licenses/>. | |
| 3294 | 18 |
| 4167 | 19 @node Optimization |
| 3294 | 20 @chapter Optimization |
| 21 | |
| 6741 | 22 Octave comes with support for solving various kinds of optimization |
|
9068
5d3059e2a34c
Cleanup documentation for optim.texi, set.texi
Rik <rdrider0-list@yahoo.com>
parents:
8920
diff
changeset
|
23 problems. Specifically Octave can solve problems in Linear Programming, |
| 6741 | 24 Quadratic Programming, Nonlinear Programming, and Linear Least Squares |
| 25 Minimization. | |
| 26 | |
| 3294 | 27 @menu |
|
17152
f2a8592b8fbd
doc: Shorten some long subsection names in Manual.
Rik <rik@octave.org>
parents:
14138
diff
changeset
|
28 * Linear Programming:: |
|
f2a8592b8fbd
doc: Shorten some long subsection names in Manual.
Rik <rik@octave.org>
parents:
14138
diff
changeset
|
29 * Quadratic Programming:: |
|
f2a8592b8fbd
doc: Shorten some long subsection names in Manual.
Rik <rik@octave.org>
parents:
14138
diff
changeset
|
30 * Nonlinear Programming:: |
|
f2a8592b8fbd
doc: Shorten some long subsection names in Manual.
Rik <rik@octave.org>
parents:
14138
diff
changeset
|
31 * Linear Least Squares:: |
| 3294 | 32 @end menu |
| 33 | |
| 34 @c @cindex linear programming | |
| 35 @cindex quadratic programming | |
| 36 @cindex nonlinear programming | |
| 37 @cindex optimization | |
| 38 @cindex LP | |
| 39 @cindex QP | |
| 40 @cindex NLP | |
| 41 | |
| 4246 | 42 @node Linear Programming |
| 43 @section Linear Programming | |
| 44 | |
| 6741 | 45 Octave can solve Linear Programming problems using the @code{glpk} |
| 46 function. That is, Octave can solve | |
| 47 | |
| 48 @tex | |
| 49 $$ | |
| 50 \min_x c^T x | |
| 51 $$ | |
| 52 @end tex | |
| 53 @ifnottex | |
|
10828
322f43e0e170
Grammarcheck .txi documentation files.
Rik <octave@nomad.inbox5.com>
parents:
9642
diff
changeset
|
54 |
| 6741 | 55 @example |
| 56 min C'*x | |
| 57 @end example | |
|
10828
322f43e0e170
Grammarcheck .txi documentation files.
Rik <octave@nomad.inbox5.com>
parents:
9642
diff
changeset
|
58 |
| 6741 | 59 @end ifnottex |
| 60 subject to the linear constraints | |
| 61 @tex | |
| 62 $Ax = b$ where $x \geq 0$. | |
| 63 @end tex | |
| 64 @ifnottex | |
|
10828
322f43e0e170
Grammarcheck .txi documentation files.
Rik <octave@nomad.inbox5.com>
parents:
9642
diff
changeset
|
65 @math{A*x = b} where @math{x @geq{} 0}. |
| 6741 | 66 @end ifnottex |
| 67 | |
| 68 @noindent | |
| 69 The @code{glpk} function also supports variations of this problem. | |
| 70 | |
| 6502 | 71 @DOCSTRING(glpk) |
| 72 | |
| 4167 | 73 @node Quadratic Programming |
| 3294 | 74 @section Quadratic Programming |
| 75 | |
| 6741 | 76 Octave can also solve Quadratic Programming problems, this is |
| 77 @tex | |
| 78 $$ | |
| 79 \min_x {1 \over 2} x^T H x + x^T q | |
| 80 $$ | |
| 81 @end tex | |
| 82 @ifnottex | |
|
10828
322f43e0e170
Grammarcheck .txi documentation files.
Rik <octave@nomad.inbox5.com>
parents:
9642
diff
changeset
|
83 |
| 6741 | 84 @example |
| 85 min 0.5 x'*H*x + x'*q | |
| 86 @end example | |
|
10828
322f43e0e170
Grammarcheck .txi documentation files.
Rik <octave@nomad.inbox5.com>
parents:
9642
diff
changeset
|
87 |
| 6741 | 88 @end ifnottex |
| 89 subject to | |
| 90 @tex | |
| 91 $$ | |
| 92 Ax = b \qquad lb \leq x \leq ub \qquad A_{lb} \leq A_{in} \leq A_{ub} | |
| 93 $$ | |
| 94 @end tex | |
| 95 @ifnottex | |
|
10828
322f43e0e170
Grammarcheck .txi documentation files.
Rik <octave@nomad.inbox5.com>
parents:
9642
diff
changeset
|
96 |
| 6741 | 97 @example |
|
9068
5d3059e2a34c
Cleanup documentation for optim.texi, set.texi
Rik <rdrider0-list@yahoo.com>
parents:
8920
diff
changeset
|
98 @group |
| 6741 | 99 A*x = b |
| 100 lb <= x <= ub | |
| 101 A_lb <= A_in*x <= A_ub | |
|
9068
5d3059e2a34c
Cleanup documentation for optim.texi, set.texi
Rik <rdrider0-list@yahoo.com>
parents:
8920
diff
changeset
|
102 @end group |
| 6741 | 103 @end example |
|
10828
322f43e0e170
Grammarcheck .txi documentation files.
Rik <octave@nomad.inbox5.com>
parents:
9642
diff
changeset
|
104 |
| 6741 | 105 @end ifnottex |
| 106 | |
| 6502 | 107 @DOCSTRING(qp) |
| 108 | |
|
9642
2ab5ace09d8b
doc/interpreter/optim.txi: document pqpnonneg
John W. Eaton <jwe@octave.org>
parents:
9209
diff
changeset
|
109 @DOCSTRING(pqpnonneg) |
|
2ab5ace09d8b
doc/interpreter/optim.txi: document pqpnonneg
John W. Eaton <jwe@octave.org>
parents:
9209
diff
changeset
|
110 |
| 4167 | 111 @node Nonlinear Programming |
| 3294 | 112 @section Nonlinear Programming |
| 113 | |
| 6741 | 114 Octave can also perform general nonlinear minimization using a |
| 115 successive quadratic programming solver. | |
| 116 | |
| 6502 | 117 @DOCSTRING(sqp) |
| 118 | |
| 4167 | 119 @node Linear Least Squares |
| 3294 | 120 @section Linear Least Squares |
| 121 | |
| 6741 | 122 Octave also supports linear least squares minimization. That is, |
| 6939 | 123 Octave can find the parameter @math{b} such that the model |
| 6741 | 124 @tex |
| 125 $y = xb$ | |
| 126 @end tex | |
| 127 @ifnottex | |
| 128 @math{y = x*b} | |
| 129 @end ifnottex | |
| 8828 | 130 fits data @math{(x,y)} as well as possible, assuming zero-mean |
| 6741 | 131 Gaussian noise. If the noise is assumed to be isotropic the problem |
| 132 can be solved using the @samp{\} or @samp{/} operators, or the @code{ols} | |
| 133 function. In the general case where the noise is assumed to be anisotropic | |
| 134 the @code{gls} is needed. | |
| 135 | |
| 136 @DOCSTRING(ols) | |
| 137 | |
| 3368 | 138 @DOCSTRING(gls) |
| 3294 | 139 |
|
7984
bbaa5d7d0143
Some documentation updates
David Bateman <dbateman@free.fr>
parents:
7018
diff
changeset
|
140 @DOCSTRING(lsqnonneg) |
|
8286
6f2d95255911
fix @seealso references to point to existing anchors
Thorsten Meyer <thorsten.meyier@gmx.de>
parents:
7984
diff
changeset
|
141 |
|
19105
c9113e28fae8
New lscov function (bug #43118)
Pantxo Diribarne <pantxo.diribarne@gmail.com>
parents:
17744
diff
changeset
|
142 @DOCSTRING(lscov) |
|
c9113e28fae8
New lscov function (bug #43118)
Pantxo Diribarne <pantxo.diribarne@gmail.com>
parents:
17744
diff
changeset
|
143 |
|
8286
6f2d95255911
fix @seealso references to point to existing anchors
Thorsten Meyer <thorsten.meyier@gmx.de>
parents:
7984
diff
changeset
|
144 @DOCSTRING(optimset) |
|
8817
03b7f618ab3d
include docstrings for new functions in the manual
John W. Eaton <jwe@octave.org>
parents:
8286
diff
changeset
|
145 |
|
03b7f618ab3d
include docstrings for new functions in the manual
John W. Eaton <jwe@octave.org>
parents:
8286
diff
changeset
|
146 @DOCSTRING(optimget) |