Extragradient methods for solving non-Lipschitzian pseudo-monotone variational inequalities

被引：49

作者：

Duong Viet Thong ^{[1
]}

Gibali, Aviv ^{[2
,3
]}

机构：

[1] Ton Duc Thang Univ, Fac Math & Stat, Appl Anal Res Grp, Ho Chi Minh City, Vietnam

[2] ORT Braude Coll, Dept Math, IL-2161002 Karmiel, Israel

[3] Univ Haifa, Ctr Math & Sci Computat, IL-3498838 Haifa, Israel

来源：

JOURNAL OF FIXED POINT THEORY AND APPLICATIONS | 2019年 / 21卷 / 01期

关键词：

Extragradient method; Halpern method; variational inequality; pseudo-monotone operator; COMPLEMENTARITY-PROBLEMS; STRONG-CONVERGENCE; WEAK-CONVERGENCE; ALGORITHMS; OPERATORS; POINT;

D O I：

10.1007/s11784-018-0656-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The purpose of this paper is to study and analyze two new extragradient methods for solving non-Lipschitzian and pseudo-monotone variational inequalities in real Hilbert spaces. Under suitable conditions, weak and strong convergence theorems of the proposed methods are established. We present academic and numerical examples for illustrating the behavior of the proposed algorithms.

引用

页数：19

共 36 条

[1]

Antipin A. S., 1976, Ekonom. i Mat. Metody, V12, P1164

[2] The Subgradient Extragradient Method for Solving Variational Inequalities in Hilbert Space [J].

Censor, Y. ;

Gibali, A. ;

Reich, S. .

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2011, 148 (02) :318-335

[3] Strong convergence of subgradient extragradient methods for the variational inequality problem in Hilbert space [J].

Censor, Yair ;

Gibali, Aviv ;

Reich, Simeon .

OPTIMIZATION METHODS & SOFTWARE, 2011, 26 (4-5) :827-845

[4] Algorithms for the Split Variational Inequality Problem [J].

Censor, Yair ;

Gibali, Aviv ;

Reich, Simeon .

NUMERICAL ALGORITHMS, 2012, 59 (02) :301-323

[5] Extensions of Korpelevich's extragradient method for the variational inequality problem in Euclidean space [J].

Censor, Yair ;

Gibali, Aviv ;

Reich, Simeon .

OPTIMIZATION, 2012, 61 (09) :1119-1132

[6] PSEUDOMONOTONE COMPLEMENTARITY-PROBLEMS IN HILBERT-SPACE [J].

COTTLE, RW ;

YAO, JC .

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 1992, 75 (02) :281-295

[7] Convergence of the Modified Extragradient Method for Variational Inequalities with Non-Lipschitz Operators [J].

Denisov S.V. ;

Semenov V.V. ;

Chabak L.M. .

Cybernetics and Systems Analysis, 2015, 51 (05) :757-765

[8] Inertial extragradient algorithms for strongly pseudomonotone variational inequalities [J].

Duong Viet Thong ;

Dang Van Hieu .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2018, 341 :80-98

[9] Modified subgradient extragradient method for variational inequality problems [J].

Duong Viet Thong ;

Dang Van Hieu .

NUMERICAL ALGORITHMS, 2018, 79 (02) :597-610

[10]

Facchinei F, 2003, SPRING S OPERAT RES, V1

← 1 2 3 4 →