Modified Tseng's extragradient methods for variational inequality on Hadamard manifolds

2019 ◽  
pp. 1-14 ◽  
Author(s):  
Junfeng Chen ◽  
Sanyang Liu ◽  
Xiaokai Chang
Keyword(s):  
Variational Inequality ◽  
Hadamard Manifolds ◽  
Extragradient Methods

scholarly journals New Tseng’s extragradient methods for pseudomonotone variational inequality problems in Hadamard manifolds

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Konrawut Khammahawong ◽  
Poom Kumam ◽  
Parin Chaipunya ◽  
Somyot Plubtieng
Keyword(s):  
Variational Inequality ◽  
Numerical Experiments ◽  
Vector Fields ◽  
Variational Inequality Problem ◽  
Variational Inequality Problems ◽  
Hadamard Manifolds ◽  
Extragradient Methods ◽  
Continuous Vector ◽  
Inequality Problem ◽  
Lipschitz Continuous

AbstractWe propose Tseng’s extragradient methods for finding a solution of variational inequality problems associated with pseudomonotone vector fields in Hadamard manifolds. Under standard assumptions such as pseudomonotone and Lipschitz continuous vector fields, we prove that any sequence generated by the proposed methods converges to a solution of variational inequality problem, whenever it exits. Moreover, we give some numerical experiments to illustrate our main results.

scholarly journals Parallel Tseng’s Extragradient Methods for Solving Systems of Variational Inequalities on Hadamard Manifolds

Symmetry ◽  
2019 ◽  
Vol 12 (1) ◽  
pp. 43
Author(s):  
Lu-Chuan Ceng ◽  
Yekini Shehu ◽  
Yuanheng Wang
Keyword(s):  
Variational Inequalities ◽  
Parallel Algorithms ◽  
Line Search ◽  
Vector Fields ◽  
Hadamard Manifolds ◽  
Monotone Variational Inequalities ◽  
Extragradient Methods ◽  
Lipschitz Constants ◽  
Systems Of Variational Inequalities

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.

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