Splitting-type method for systems of variational inequalities

2006 ◽  
Vol 33 (2) ◽  
pp. 520-534 ◽  
Author(s):  
I.V. Konnov
Keyword(s):  
Variational Inequalities ◽  
Type Method ◽  
Splitting Type ◽  
Systems Of Variational Inequalities

scholarly journals An Efficient Parallel Extragradient Method for Systems of Variational Inequalities Involving Fixed Points of Demicontractive Mappings

Symmetry ◽  
2020 ◽  
Vol 12 (11) ◽  
pp. 1915
Author(s):  
Lateef Olakunle Jolaoso ◽  
Maggie Aphane
Keyword(s):  
Variational Inequalities ◽  
Hilbert Spaces ◽  
Line Search ◽  
Convex Combination ◽  
Extragradient Method ◽  
Convergence Result ◽  
Armijo Line Search ◽  
Systems Of Variational Inequalities ◽  
Demicontractive Mappings ◽  
The Cost

Herein, we present a new parallel extragradient method for solving systems of variational inequalities and common fixed point problems for demicontractive mappings in real Hilbert spaces. The algorithm determines the next iterate by computing a computationally inexpensive projection onto a sub-level set which is constructed using a convex combination of finite functions and an Armijo line-search procedure. A strong convergence result is proved without the need for the assumption of Lipschitz continuity on the cost operators of the variational inequalities. Finally, some numerical experiments are performed to illustrate the performance of the proposed method.

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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