Find minimum of function using pattern search
x = patternsearch(fun,x0)
x = patternsearch(fun,x0,A,b)
x = patternsearch(fun,x0,A,b,Aeq,beq)
x = patternsearch(fun,x0,A,b,Aeq,beq,lb,ub)
x = patternsearch(fun,x0,A,b,Aeq,beq,lb,ub,nonlcon)
x = patternsearch(fun,x0,A,b,Aeq,beq,lb,ub,nonlcon,options)
x = patternsearch(problem)
[x,fval]
= patternsearch(___)
[x,fval,exitflag,output]
= patternsearch(___)
finds
a local minimum, x
= patternsearch(fun
,x0
)x
, to the function handle fun
that
computes the values of the objective function. x0
is
a real vector specifying an initial point for the pattern search algorithm.
Note: Passing Extra Parameters (Optimization Toolbox) explains how to pass extra parameters to the objective function and nonlinear constraint functions, if necessary. |
defines
a set of lower and upper bounds on the design variables in x
= patternsearch(fun
,x0
,A
,b
,Aeq
,beq
,lb
,ub
)x
,
so that the solution is always in the range lb
≤ x
≤ ub
.
If no linear equalities exist, set Aeq = []
and beq
= []
. If x(i)
has no lower bound, set lb(i)
= -Inf
. If x(i)
has no upper bound, set ub(i)
= Inf
.
finds
the minimum for x
= patternsearch(problem
)problem
, where problem
is
a structure described in Input Arguments.
Create the problem
structure by exporting a problem
from Optimization app, as described in Exporting Your Work (Optimization Toolbox).
By default, patternsearch
looks for a minimum
based on an adaptive mesh that, in the absence of linear constraints,
is aligned with the coordinate directions. See What Is Direct Search? and How Pattern Search Polling Works.
[1] Audet, Charles, and J. E. Dennis Jr. "Analysis of Generalized Pattern Searches." SIAM Journal on Optimization. Volume 13, Number 3, 2003, pp. 889–903.
[2] Conn, A. R., N. I. M. Gould, and Ph. L. Toint. "A Globally Convergent Augmented Lagrangian Barrier Algorithm for Optimization with General Inequality Constraints and Simple Bounds." Mathematics of Computation. Volume 66, Number 217, 1997, pp. 261–288.
[3] Abramson, Mark A. Pattern Search Filter Algorithms for Mixed Variable General Constrained Optimization Problems. Ph.D. Thesis, Department of Computational and Applied Mathematics, Rice University, August 2002.
[4] Abramson, Mark A., Charles Audet, J. E. Dennis, Jr., and Sebastien Le Digabel. "ORTHOMADS: A deterministic MADS instance with orthogonal directions." SIAM Journal on Optimization. Volume 20, Number 2, 2009, pp. 948–966.
[5] Kolda, Tamara G., Robert Michael Lewis, and Virginia Torczon. "Optimization by direct search: new perspectives on some classical and modern methods." SIAM Review. Volume 45, Issue 3, 2003, pp. 385–482.
[6] Kolda, Tamara G., Robert Michael Lewis, and Virginia Torczon. "A generating set direct search augmented Lagrangian algorithm for optimization with a combination of general and linear constraints." Technical Report SAND2006-5315, Sandia National Laboratories, August 2006.
[7] Lewis, Robert Michael, Anne Shepherd, and Virginia Torczon. "Implementing generating set search methods for linearly constrained minimization." SIAM Journal on Scientific Computing. Volume 29, Issue 6, 2007, pp. 2507–2530.
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