Strong Convergence of the Halpern Subgradient Extragradient Method for Solving Variational Inequalities in Hilbert Spaces

被引：242

作者：

Kraikaew, Rapeepan ^{[1
]}

Saejung, Satit ^{[1
]}

机构：

[1] Khon Kaen Univ, Dept Math, Fac Sci, Khon Kaen 40002, Thailand

来源：

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS | 2014年 / 163卷 / 02期

关键词：

Subgradient extragradient method; Halpern method; Variational inequality; Quasi-nonexpansive mapping; Fixed point; BANACH-SPACES; NONEXPANSIVE-MAPPINGS; FIXED-POINTS; COMMON SOLUTIONS; APPROXIMATION; OPERATORS; SYSTEMS;

D O I：

10.1007/s10957-013-0494-2

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：

Building upon the subgradient extragradient method proposed by Censor et al., we prove the strong convergence of the iterative sequence generated by a modification of this method by means of the Halpern method. We also consider the problem of finding a common element of the solution set of a variational inequality and the fixed-point set of a quasi-nonexpansive mapping with a demiclosedness property.

引用

页码：399 / 412

页数：14

共 50 条

[1] Strong Convergence of the Halpern Subgradient Extragradient Method for Solving Variational Inequalities in Hilbert Spaces
Rapeepan Kraikaew
Satit Saejung
[J]. Journal of Optimization Theory and Applications, 2014, 163 : 399 - 412
[2] Strong convergence of the Halpern subgradient extragradient method for solving variational inequalities in Banach spaces
Liu, Ying
[J]. JOURNAL OF NONLINEAR SCIENCES AND APPLICATIONS, 2017, 10 (02): : 395 - 409
[3] Two strong convergence subgradient extragradient methods for solving variational inequalities in Hilbert spaces
Duong Viet Thong
Gibali, Aviv
[J]. JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS, 2019, 36 (01) : 299 - 321
[4] Two strong convergence subgradient extragradient methods for solving variational inequalities in Hilbert spaces
Duong Viet Thong
Aviv Gibali
[J]. Japan Journal of Industrial and Applied Mathematics, 2019, 36 : 299 - 321
[5] Strong convergence of subgradient extragradient method with regularization for solving variational inequalities
Dang Van Hieu
Pham Ky Anh
Le Dung Muu
[J]. Optimization and Engineering, 2021, 22 : 2575 - 2602
[6] Strong convergence of subgradient extragradient method with regularization for solving variational inequalities
Hieu, Dang Van
Anh, Pham Ky
Muu, Le Dung
[J]. OPTIMIZATION AND ENGINEERING, 2021, 22 (04) : 2575 - 2602
[7] The Subgradient Extragradient Method for Solving Variational Inequalities in Hilbert Space
Y. Censor
A. Gibali
S. Reich
[J]. Journal of Optimization Theory and Applications, 2011, 148 : 318 - 335
[8] The Subgradient Extragradient Method for Solving Variational Inequalities in Hilbert Space
Censor, Y.
Gibali, A.
Reich, S.
[J]. JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2011, 148 (02) : 318 - 335
[9] Improved subgradient extragradient methods for solving pseudomonotone variational inequalities in Hilbert spaces
Duong Viet Thong
Phan Tu Vuong
[J]. APPLIED NUMERICAL MATHEMATICS, 2021, 163 : 221 - 238
[10] Strong convergence of the tseng extragradient method for solving variational inequalities
Tong M.-Y.
Tian M.
[J]. Applied Set-Valued Analysis and Optimization, 2020, 2 (01): : 19 - 33

← 1 2 3 4 5 →