patternsearch
Find minimum of function using pattern search
Syntax
Description
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 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
.
Examples
Input Arguments
Output Arguments
Algorithms
By default and in the absence of linear constraints, patternsearch
looks
for a minimum based on an adaptive mesh that is aligned with the coordinate directions. See
What Is Direct Search? and How Pattern Search Polling Works.
When you set the Algorithm
option to "nups"
or one
of its variants, patternsearch
uses the algorithm described in Nonuniform Pattern Search (NUPS) Algorithm. This algorithm is different
from the default algorithm in several ways; for example, it has fewer options to
set.
Alternative Functionality
App
The Optimize Live Editor task provides a visual interface for patternsearch
.
References
[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.
Extended Capabilities
Version History
Introduced before R2006a
See Also
ga
| optimoptions
| paretosearch
| Optimize
Topics
- Optimize Using the GPS Algorithm
- Coding and Minimizing an Objective Function Using Pattern Search
- Constrained Minimization Using Pattern Search, Solver-Based
- Effects of Pattern Search Options
- Optimize ODEs in Parallel
- Pattern Search Climbs Mount Washington
- Optimization Workflow
- What Is Direct Search?
- Pattern Search Terminology
- How Pattern Search Polling Works
- Polling Types
- Search and Poll