Mercurial > hg > octave-nkf
annotate doc/interpreter/optim.txi @ 9642:2ab5ace09d8b
doc/interpreter/optim.txi: document pqpnonneg
| author | John W. Eaton <jwe@octave.org> |
|---|---|
| date | Mon, 14 Sep 2009 22:24:43 -0400 |
| parents | 923c7cb7f13f |
| children | 322f43e0e170 |
| rev | line source |
|---|---|
| 8920 | 1 @c Copyright (C) 1996, 1997, 2007, 2008, 2009 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. | |
| 9 @c | |
| 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. | |
| 14 @c | |
| 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
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Cleanup documentation for optim.texi, set.texi
Rik <rdrider0-list@yahoo.com>
parents:
8920
diff
changeset
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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 |
| 4246 | 28 * Linear Programming:: |
| 3294 | 29 * Quadratic Programming:: |
| 30 * Nonlinear Programming:: | |
| 31 * Linear Least Squares:: | |
| 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 | |
| 54 @example | |
| 55 min C'*x | |
| 56 @end example | |
| 57 @end ifnottex | |
| 58 subject to the linear constraints | |
| 59 @tex | |
| 60 $Ax = b$ where $x \geq 0$. | |
| 61 @end tex | |
| 62 @ifnottex | |
| 63 @math{A*x = b} where @math{x >= 0}. | |
| 64 @end ifnottex | |
| 65 | |
| 66 @noindent | |
| 67 The @code{glpk} function also supports variations of this problem. | |
| 68 | |
| 6502 | 69 @DOCSTRING(glpk) |
| 70 | |
| 4167 | 71 @node Quadratic Programming |
| 3294 | 72 @section Quadratic Programming |
| 73 | |
| 6741 | 74 Octave can also solve Quadratic Programming problems, this is |
| 75 @tex | |
| 76 $$ | |
| 77 \min_x {1 \over 2} x^T H x + x^T q | |
| 78 $$ | |
| 79 @end tex | |
| 80 @ifnottex | |
| 81 @example | |
| 82 min 0.5 x'*H*x + x'*q | |
| 83 @end example | |
| 84 @end ifnottex | |
| 85 subject to | |
| 86 @tex | |
| 87 $$ | |
| 88 Ax = b \qquad lb \leq x \leq ub \qquad A_{lb} \leq A_{in} \leq A_{ub} | |
| 89 $$ | |
| 90 @end tex | |
| 91 @ifnottex | |
| 92 @example | |
|
9068
5d3059e2a34c
Cleanup documentation for optim.texi, set.texi
Rik <rdrider0-list@yahoo.com>
parents:
8920
diff
changeset
|
93 @group |
| 6741 | 94 A*x = b |
| 95 lb <= x <= ub | |
| 96 A_lb <= A_in*x <= A_ub | |
|
9068
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Cleanup documentation for optim.texi, set.texi
Rik <rdrider0-list@yahoo.com>
parents:
8920
diff
changeset
|
97 @end group |
| 6741 | 98 @end example |
| 99 @end ifnottex | |
| 100 | |
| 6502 | 101 @DOCSTRING(qp) |
| 102 | |
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9642
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doc/interpreter/optim.txi: document pqpnonneg
John W. Eaton <jwe@octave.org>
parents:
9209
diff
changeset
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103 @DOCSTRING(pqpnonneg) |
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2ab5ace09d8b
doc/interpreter/optim.txi: document pqpnonneg
John W. Eaton <jwe@octave.org>
parents:
9209
diff
changeset
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104 |
| 4167 | 105 @node Nonlinear Programming |
| 3294 | 106 @section Nonlinear Programming |
| 107 | |
| 6741 | 108 Octave can also perform general nonlinear minimization using a |
| 109 successive quadratic programming solver. | |
| 110 | |
| 6502 | 111 @DOCSTRING(sqp) |
| 112 | |
| 4167 | 113 @node Linear Least Squares |
| 3294 | 114 @section Linear Least Squares |
| 115 | |
| 6741 | 116 Octave also supports linear least squares minimization. That is, |
| 6939 | 117 Octave can find the parameter @math{b} such that the model |
| 6741 | 118 @tex |
| 119 $y = xb$ | |
| 120 @end tex | |
| 121 @ifnottex | |
| 122 @math{y = x*b} | |
| 123 @end ifnottex | |
| 8828 | 124 fits data @math{(x,y)} as well as possible, assuming zero-mean |
| 6741 | 125 Gaussian noise. If the noise is assumed to be isotropic the problem |
| 126 can be solved using the @samp{\} or @samp{/} operators, or the @code{ols} | |
| 127 function. In the general case where the noise is assumed to be anisotropic | |
| 128 the @code{gls} is needed. | |
| 129 | |
| 130 @DOCSTRING(ols) | |
| 131 | |
| 3368 | 132 @DOCSTRING(gls) |
| 3294 | 133 |
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134 @DOCSTRING(lsqnonneg) |
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fix @seealso references to point to existing anchors
Thorsten Meyer <thorsten.meyier@gmx.de>
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135 |
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fix @seealso references to point to existing anchors
Thorsten Meyer <thorsten.meyier@gmx.de>
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136 @DOCSTRING(optimset) |
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include docstrings for new functions in the manual
John W. Eaton <jwe@octave.org>
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137 |
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03b7f618ab3d
include docstrings for new functions in the manual
John W. Eaton <jwe@octave.org>
parents:
8286
diff
changeset
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138 @DOCSTRING(optimget) |