Strong convergence of subgradient extragradient methods for the variational inequality problem in Hilbert space

被引：349

作者：

Censor, Yair ^{[1
]}

Gibali, Aviv ^{[2
]}

Reich, Simeon ^{[2
]}

机构：

[1] Univ Haifa, Dept Math, IL-31905 Haifa, Israel

[2] Technion Israel Inst Technol, Dept Math, IL-32000 Haifa, Israel

来源：

OPTIMIZATION METHODS & SOFTWARE | 2011年 / 26卷 / 4-5期

基金：

以色列科学基金会;

关键词：

extragradient method; Hilbert space; projection algorithm; subgradient; variational inequality; NONEXPANSIVE-MAPPINGS; PROJECTION ALGORITHMS; APPROXIMATIONS; OPTIMIZATION;

D O I：

10.1080/10556788.2010.551536

中图分类号：

TP31 [计算机软件];

学科分类号：

081202 ; 0835 ;

摘要：

We study two projection algorithms for solving the variational inequality problem in Hilbert space. One algorithm is a modified subgradient extragradient method in which an additional projection onto the intersection of two half-spaces is employed. Another algorithm is based on the shrinking projection method. We establish strong convergence theorems for both algorithms.

引用

页码：827 / 845

页数：19

共 27 条

[1]

[Anonymous], 2003, SPRINGER SERIES OPER, DOI DOI 10.1007/978-0-387-21815-16

[2] A strongly convergent reflection method for finding the projection onto the intersection of two closed convex sets in a Hilbert space [J].