Mesh adaptive direct search algorithms for mixed variable optimization

被引：106

作者：

Abramson, Mark A. ^{[1
]}

Audet, Charles ^{[2
,3
]}

Chrissis, James W. ^{[4
]}

Walston, Jennifer G. ^{[5
]}

机构：

[1] Boeing Co, Seattle, WA 98124 USA

[2] Ecole Polytech, Dept Math & Genie Ind, Montreal, PQ H3C 3A7, Canada

[3] Ecole Hautes Etud Commerciales, Gerad, Montreal, PQ H3C 3A7, Canada

[4] AF Inst Technol, Dept Operat Sci, Wright Patterson AFB, OH 45433 USA

[5] AF Logist Management Agcy, AFLMA LGY, Maxwell AFB Gunter Annex, AL 36114 USA

来源：

OPTIMIZATION LETTERS | 2009年 / 3卷 / 01期

基金：

加拿大自然科学与工程研究理事会;

关键词：

Nonlinear programming; Mesh adaptive direct search; Mixed variables; Derivative-free optimization; Convergence analysis; GENERALIZED PATTERN SEARCHES; CONSTRAINED MINIMIZATION; CONVERGENCE; DERIVATIVES;

D O I：

10.1007/s11590-008-0089-2

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

This paper introduces a new derivative-free class of mesh adaptive direct search (MADS) algorithms for solving constrained mixed variable optimization problems, in which the variables may be continuous or categorical. This new class of algorithms, called mixed variable MADS (MV-MADS), generalizes both mixed variable pattern search (MVPS) algorithms for linearly constrained mixed variable problems and MADS algorithms for general constrained problems with only continuous variables. The convergence analysis, which makes use of the Clarke nonsmooth calculus, similarly generalizes the existing theory for both MVPS and MADS algorithms, and reasonable conditions are established for ensuring convergence of a subsequence of iterates to a suitably defined stationary point in the nonsmooth and mixed variable sense.

引用

页码：35 / 47

页数：13

共 24 条

[1]

ABHISHEKAND K, 2007, ANLMCSP14340607

[2]

Abramson, 2002, THESIS RICE U

[3] Generalized pattern searches with derivative information [J].