Improvements of some projection methods for monotone nonlinear variational inequalities

被引:240
作者
He, BS [1 ]
Liao, LZ
机构
[1] Nanjing Univ, Dept Math, Nanjing 210008, Peoples R China
[2] Hong Kong Baptist Univ, Dept Math, Kowloon, Hong Kong, Peoples R China
基金
中国国家自然科学基金; 美国国家科学基金会;
关键词
monotone variational inequalities; explicit methods; implicit methods; prediction-correction methods;
D O I
10.1023/A:1013096613105
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
In this paper, we study the relationship of some projection-type methods for monotone nonlinear variational inequalities and investigate some improvements. If we refer to the Goldstein-Levitin-Polyak projection method as the explicit method, then the proximal point method is the corresponding implicit method. Consequently, the Korpelevich extragradient method can be viewed as a prediction-correction method. which uses the explicit method in the prediction step and the implicit method in the correction step. Based on the analysis in this paper, we propose a modified prediction-correction method by using better prediction and correction stepsizes. Preliminary numerical experiments indicate that the improvements are significant.
引用
收藏
页码:111 / 128
页数:18
相关论文
共 22 条
[1]  
Bertsekas Dimitri P., 1989, PARALLEL DISTRIBUTED
[2]  
BERTSEKAS DP, 1982, MATH PROGRAM STUD, V17, P139
[3]  
Glowinski R, 1984, NUMERICAL METHODS NO
[4]   CONVEX PROGRAMMING IN HILBERT SPACE [J].
GOLDSTEIN, AA .
BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1964, 70 (05) :709-&
[5]   FINITE-DIMENSIONAL VARIATIONAL INEQUALITY AND NONLINEAR COMPLEMENTARITY-PROBLEMS - A SURVEY OF THEORY, ALGORITHMS AND APPLICATIONS [J].
HARKER, PT ;
PANG, JS .
MATHEMATICAL PROGRAMMING, 1990, 48 (02) :161-220
[6]  
Harker PT., 1990, Comput Solut Nonlinear Syst Equ, V26, P265
[7]   A PROJECTION AND CONTRACTION METHOD FOR A CLASS OF LINEAR COMPLEMENTARITY-PROBLEMS AND ITS APPLICATION IN CONVEX QUADRATIC-PROGRAMMING [J].
HE, BS .
APPLIED MATHEMATICS AND OPTIMIZATION, 1992, 25 (03) :247-262
[8]  
He BS, 1997, APPL MATH OPT, V35, P69
[9]   A NEW METHOD FOR A CLASS OF LINEAR VARIATIONAL-INEQUALITIES [J].
HE, BS .
MATHEMATICAL PROGRAMMING, 1994, 66 (02) :137-144
[10]   SOLVING A CLASS OF LINEAR PROJECTION EQUATIONS [J].
HE, BS .
NUMERISCHE MATHEMATIK, 1994, 68 (01) :71-80