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annotate doc/interpreter/optim.txi @ 8920:eb63fbe60fab
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| author | John W. Eaton <jwe@octave.org> |
|---|---|
| date | Sat, 07 Mar 2009 10:41:27 -0500 |
| parents | 8463d1a2e544 |
| children | 5d3059e2a34c |
| 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 |
| 23 problems. Specifically Octave can solve problems in Linear Programming, | |
| 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 @iftex | |
| 49 @tex | |
| 50 $$ | |
| 51 \min_x c^T x | |
| 52 $$ | |
| 53 @end tex | |
| 54 @end iftex | |
| 55 @ifnottex | |
| 56 @example | |
| 57 min C'*x | |
| 58 @end example | |
| 59 @end ifnottex | |
| 60 subject to the linear constraints | |
| 61 @iftex | |
| 62 @tex | |
| 63 $Ax = b$ where $x \geq 0$. | |
| 64 @end tex | |
| 65 @end iftex | |
| 66 @ifnottex | |
| 67 @math{A*x = b} where @math{x >= 0}. | |
| 68 @end ifnottex | |
| 69 | |
| 70 @noindent | |
| 71 The @code{glpk} function also supports variations of this problem. | |
| 72 | |
| 6502 | 73 @DOCSTRING(glpk) |
| 74 | |
| 4167 | 75 @node Quadratic Programming |
| 3294 | 76 @section Quadratic Programming |
| 77 | |
| 6741 | 78 Octave can also solve Quadratic Programming problems, this is |
| 79 @iftex | |
| 80 @tex | |
| 81 $$ | |
| 82 \min_x {1 \over 2} x^T H x + x^T q | |
| 83 $$ | |
| 84 @end tex | |
| 85 @end iftex | |
| 86 @ifnottex | |
| 87 @example | |
| 88 min 0.5 x'*H*x + x'*q | |
| 89 @end example | |
| 90 @end ifnottex | |
| 91 subject to | |
| 92 @iftex | |
| 93 @tex | |
| 94 $$ | |
| 95 Ax = b \qquad lb \leq x \leq ub \qquad A_{lb} \leq A_{in} \leq A_{ub} | |
| 96 $$ | |
| 97 @end tex | |
| 98 @end iftex | |
| 99 @ifnottex | |
| 100 @example | |
| 101 A*x = b | |
| 102 lb <= x <= ub | |
| 103 A_lb <= A_in*x <= A_ub | |
| 104 @end example | |
| 105 @end ifnottex | |
| 106 | |
| 6502 | 107 @DOCSTRING(qp) |
| 108 | |
| 4167 | 109 @node Nonlinear Programming |
| 3294 | 110 @section Nonlinear Programming |
| 111 | |
| 6741 | 112 Octave can also perform general nonlinear minimization using a |
| 113 successive quadratic programming solver. | |
| 114 | |
| 6502 | 115 @DOCSTRING(sqp) |
| 116 | |
| 4167 | 117 @node Linear Least Squares |
| 3294 | 118 @section Linear Least Squares |
| 119 | |
| 6741 | 120 Octave also supports linear least squares minimization. That is, |
| 6939 | 121 Octave can find the parameter @math{b} such that the model |
| 6741 | 122 @iftex |
| 123 @tex | |
| 124 $y = xb$ | |
| 125 @end tex | |
| 126 @end iftex | |
| 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 |
|
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Some documentation updates
David Bateman <dbateman@free.fr>
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140 @DOCSTRING(lsqnonneg) |
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fix @seealso references to point to existing anchors
Thorsten Meyer <thorsten.meyier@gmx.de>
parents:
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changeset
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141 |
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6f2d95255911
fix @seealso references to point to existing anchors
Thorsten Meyer <thorsten.meyier@gmx.de>
parents:
7984
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changeset
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142 @DOCSTRING(optimset) |
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8817
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include docstrings for new functions in the manual
John W. Eaton <jwe@octave.org>
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143 |
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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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144 @DOCSTRING(optimget) |