Pattern search algorithms for bound constrained minimization

被引:329
作者
Lewis, RM
Torczon, V
机构
[1] NASA, Langley Res Ctr, Inst Comp Applicat Sci & Engn, Hampton, VA 23681 USA
[2] Coll William & Mary, Dept Comp Sci, Williamsburg, VA 23187 USA
关键词
bound constrained optimization; convergence analysis; pattern search methods; direct search methods; globalization strategies; alternating variable search; axial relaxation; local variation; coordinate search; evolutionary operation; multidirectional search;
D O I
10.1137/S1052623496300507
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We present a convergence theory for pattern search methods for solving bound constrained nonlinear programs. The analysis relies on the abstract structure of pattern search methods and an understanding of how the pattern interacts with the bound constraints. This analysis makes it possible to develop pattern search methods for bound constrained problems while only slightly restricting the flexibility present in pattern search methods for unconstrained problems. We prove global convergence despite the fact that pattern search methods do not have explicit information concerning the gradient and its projection onto the feasible region and consequently are unable to enforce explicitly a notion of sufficient feasible decrease.
引用
收藏
页码:1082 / 1099
页数:18
相关论文
共 18 条
[1]  
[Anonymous], APPLIED STATISTICS
[2]   ON THE EXPERIMENTAL ATTAINMENT OF OPTIMUM CONDITIONS [J].
BOX, GEP ;
WILSON, KB .
JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY, 1951, 13 (01) :1-45
[3]  
BOXMJ, 1969, ICI MONOGRAPH, V5
[4]   ON THE IDENTIFICATION OF ACTIVE CONSTRAINTS [J].
BURKE, JV ;
MORE, JJ .
SIAM JOURNAL ON NUMERICAL ANALYSIS, 1988, 25 (05) :1197-1211
[5]   PROJECTED GRADIENT METHODS FOR LINEARLY CONSTRAINED PROBLEMS [J].
CALAMAI, PH ;
MORE, JJ .
MATHEMATICAL PROGRAMMING, 1987, 39 (01) :93-116
[6]   GLOBAL CONVERGENCE OF A CLASS OF TRUST REGION ALGORITHMS FOR OPTIMIZATION WITH SIMPLE BOUNDS [J].
CONN, AR ;
GOULD, NIM ;
TOINT, PL .
SIAM JOURNAL ON NUMERICAL ANALYSIS, 1988, 25 (02) :433-460
[7]   DIRECT SEARCH METHODS ON PARALLEL MACHINES [J].
Dennis, J. E., Jr. ;
Torczon, Virginia .
SIAM JOURNAL ON OPTIMIZATION, 1991, 1 (04) :448-474
[9]  
HOOKE R, 1961, J ACM, V8, P212, DOI 10.1145/321062.321069
[10]   SIMPAT - SELF-BOUNDING DIRECT SEARCH METHOD FOR OPTIMIZATION [J].
KEEFER, DL .
INDUSTRIAL & ENGINEERING CHEMISTRY PROCESS DESIGN AND DEVELOPMENT, 1973, 12 (01) :92-99