Parallel Tseng's Extragradient Methods for Solving Systems of Variational Inequalities on Hadamard Manifolds

被引：4

作者：

Ceng, Lu-Chuan ^{[1
]}

Shehu, Yekini ^{[2
]}

Wang, Yuanheng ^{[2
]}

机构：

[1] Shanghai Normal Univ, Dept Math, Shanghai 200234, Peoples R China

[2] Zhejiang Normal Univ, Dept Math, Jinhua 321004, Zhejiang, Peoples R China

来源：

SYMMETRY-BASEL | 2020年 / 12卷 / 01期

基金：

中国国家自然科学基金;

关键词：

system of variational inequalities; extragradient method; Hadamard manifolds; monotone vector fields; STRONG-CONVERGENCE THEOREMS; PROXIMAL POINT ALGORITHM; MONOTONE VECTOR-FIELDS; ACCRETIVE-OPERATORS; NONEXPANSIVE-MAPPINGS; ITERATIVE ALGORITHMS; COMMON SOLUTIONS; FIXED-POINTS; EQUILIBRIUM;

D O I：

10.3390/sym12010043

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

The aim of this article is to study two efficient parallel algorithms for obtaining a solution to a system of monotone variational inequalities (SVI) on Hadamard manifolds. The parallel algorithms are inspired by Tseng's extragradient techniques with new step sizes, which are established without the knowledge of the Lipschitz constants of the operators and line-search. Under the monotonicity assumptions regarding the underlying vector fields, one proves that the sequences generated by the methods converge to a solution of the monotone SVI whenever it exists.

引用

页数：16

共 38 条

[1] Regularization of proximal point algorithms in Hadamard manifolds [J].

Ansari, Qamrul Hasan ;

Babu, Feeroz ;

Yao, Jen-Chih .

JOURNAL OF FIXED POINT THEORY AND APPLICATIONS, 2019, 21 (01)

[2]

Bin Dehaish BA, 2015, J NONLINEAR CONVEX A, V16, P1321

[3]

Bridson M.R., 2013, METRIC SPACES NONPOS, V319

[4]

CENG LC, 2019, MATHEMATICS-BASEL, V7, DOI DOI 10.3390/math7100933

[5]

CENG LC, 2019, OPTIMIZATION 0727, DOI DOI 10.1080/02331934.2019.1647203

[6] Strong convergence theorems by a relaxed extragradient method for a general system of variational inequalities [J].

Ceng, Lu-Chuan ;

Wang, Chang-yu ;

Yao, Jen-Chih .

MATHEMATICAL METHODS OF OPERATIONS RESEARCH, 2008, 67 (03) :375-390

[7] Composite inertial subgradient extragradient methods for variational inequalities and fixed point problems [J].

Ceng, Lu-Chuan ;

Yuan, Qing .

JOURNAL OF INEQUALITIES AND APPLICATIONS, 2019, 2019 (01)

[8] SYSTEMS OF VARIATIONAL INEQUALITIES WITH HIERARCHICAL VARIATIONAL INEQUALITY CONSTRAINTS FOR LIPSCHITZIAN PSEUDOCONTRACTIONS [J].

Ceng, Lu-Chuan ;

Petrusel, Adrian ;

Yao, Jen-Chih ;

Yao, Yonghong .

FIXED POINT THEORY, 2019, 20 (01) :113-133

[9] HYBRID VISCOSITY EXTRAGRADIENT METHOD FOR SYSTEMS OF VARIATIONAL INEQUALITIES, FIXED POINTS OF NONEXPANSIVE MAPPINGS, ZERO POINTS OF ACCRETIVE OPERATORS IN BANACH SPACES [J].

Ceng, Lu-Chuan ;

Petrusel, Adrian ;

Yao, Jen-Chih ;

Yao, Yonghong .

FIXED POINT THEORY, 2018, 19 (02) :487-+

[10] 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

← 1 2 3 4 →