NONMONOTONIC TRUST REGION ALGORITHM

被引:253
作者
DENG, NY
XIAO, Y
ZHOU, FJ
机构
[1] BEIJING POLYTECH UNIV,DEPT APPL MATH,BEIJING,PEOPLES R CHINA
[2] TSING HUA UNIV,DEPT APPL MATH,BEIJING,PEOPLES R CHINA
关键词
UNCONSTRAINED OPTIMIZATION; TRUST REGION METHOD; NONMONOTONE METHOD; CONVERGENCE;
D O I
10.1007/BF00939608
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
A nonmonotonic trust region method for unconstrained optimization problems is presented. Although the method allows the sequence of values of the objective function to be nonmonotonic, convergence properties similar to those for the usual trust region method are proved under certain conditions, including conditions on the approximate solutions to the subproblem. To make the solution satisfy these conditions, an algorithm to solve the subproblem is also established. Finally, some numerical results are reported which show that the nonmonotonic trust region method is superior to the usual trust region method according to both the number of gradient evaluations and the number of function evaluations.
引用
收藏
页码:259 / 285
页数:27
相关论文
共 10 条
[1]  
CHAMBERLAIN RM, 1986, MATH PROGRAMMING STU, V26, P1
[2]   2 NEW UNCONSTRAINED OPTIMIZATION ALGORITHMS WHICH USE FUNCTION AND GRADIENT VALUES [J].
DENNIS, JE ;
MEI, HHW .
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 1979, 28 (04) :453-482
[3]  
DENNIS JE, 1983, NUMERICAL METHODS UN
[4]   A TRUNCATED NEWTON METHOD WITH NONMONOTONE LINE SEARCH FOR UNCONSTRAINED OPTIMIZATION [J].
GRIPPO, L ;
LAMPARIELLO, F ;
LUCIDI, S .
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 1989, 60 (03) :401-419
[5]   A NONMONOTONE LINE SEARCH TECHNIQUE FOR NEWTON METHOD [J].
GRIPPO, L ;
LAMPARIELLO, F ;
LUCIDI, S .
SIAM JOURNAL ON NUMERICAL ANALYSIS, 1986, 23 (04) :707-716
[6]  
More JJ, 1983, MATH PROGRAMMING STA, P258
[7]   A FAMILY OF TRUST-REGION-BASED ALGORITHMS FOR UNCONSTRAINED MINIMIZATION WITH STRONG GLOBAL CONVERGENCE PROPERTIES [J].
SHULTZ, GA ;
SCHNABEL, RB ;
BYRD, RH .
SIAM JOURNAL ON NUMERICAL ANALYSIS, 1985, 22 (01) :47-67
[8]   NEWTON METHOD WITH A MODEL TRUST REGION MODIFICATION [J].
SORENSEN, DC .
SIAM JOURNAL ON NUMERICAL ANALYSIS, 1982, 19 (02) :409-426
[10]  
White T.J., 1975, NONLINEAR PROGRAMMIN, P315, DOI 10.1016/B978-0-12-372180-8.50042-1