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view doc/interpreter/optim.txi @ 6741:00116015904d
[project @ 2007-06-18 16:07:14 by jwe]
author | jwe |
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date | Mon, 18 Jun 2007 16:07:14 +0000 |
parents | 6ab0a8767780 |
children | 083721ae3dfa |
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@c Copyright (C) 1996, 1997 John W. Eaton @c This is part of the Octave manual. @c For copying conditions, see the file gpl.texi. @node Optimization @chapter Optimization Octave comes with support for solving various kinds of optimization problems. Specifically Octave can solve problems in Linear Programming, Quadratic Programming, Nonlinear Programming, and Linear Least Squares Minimization. @menu * Linear Programming:: * Quadratic Programming:: * Nonlinear Programming:: * Linear Least Squares:: @end menu @c @cindex linear programming @cindex quadratic programming @cindex nonlinear programming @cindex optimization @cindex LP @cindex QP @cindex NLP @node Linear Programming @section Linear Programming Octave can solve Linear Programming problems using the @code{glpk} function. That is, Octave can solve @iftex @tex $$ \min_x c^T x $$ @end tex @end iftex @ifnottex @example min C'*x @end example @end ifnottex subject to the linear constraints @iftex @tex $Ax = b$ where $x \geq 0$. @end tex @end iftex @ifnottex @math{A*x = b} where @math{x >= 0}. @end ifnottex @noindent The @code{glpk} function also supports variations of this problem. @DOCSTRING(glpk) @node Quadratic Programming @section Quadratic Programming Octave can also solve Quadratic Programming problems, this is @iftex @tex $$ \min_x {1 \over 2} x^T H x + x^T q $$ @end tex @end iftex @ifnottex @example min 0.5 x'*H*x + x'*q @end example @end ifnottex subject to @iftex @tex $$ Ax = b \qquad lb \leq x \leq ub \qquad A_{lb} \leq A_{in} \leq A_{ub} $$ @end tex @end iftex @ifnottex @example A*x = b lb <= x <= ub A_lb <= A_in*x <= A_ub @end example @end ifnottex @DOCSTRING(qp) @node Nonlinear Programming @section Nonlinear Programming Octave can also perform general nonlinear minimization using a successive quadratic programming solver. @DOCSTRING(sqp) @node Linear Least Squares @section Linear Least Squares Octave also supports linear least squares minimization. That is, Octave can find the parameter @math{b} such the the model @iftex @tex $y = xb$ @end tex @end iftex @ifnottex @math{y = x*b} @end ifnottex fits data @math{(x,y)} as good as possible, assuming zero-mean Gaussian noise. If the noise is assumed to be isotropic the problem can be solved using the @samp{\} or @samp{/} operators, or the @code{ols} function. In the general case where the noise is assumed to be anisotropic the @code{gls} is needed. @DOCSTRING(ols) @DOCSTRING(gls)