scholarly journals On the convergence properties of non-Euclidean extragradient methods for variational inequalities with generalized monotone operators

2014 ◽  
Vol 60 (2) ◽  
pp. 277-310 ◽  
Author(s):  
Cong D. Dang ◽  
Guanghui Lan
Keyword(s):  
Variational Inequalities ◽  
Monotone Operators ◽  
Convergence Properties ◽  
Extragradient Methods

Modified Extragradient Methods for a System of Variational Inequalities in Banach Spaces

2009 ◽  
Vol 110 (3) ◽  
pp. 1211-1224 ◽  
Author(s):  
Yonghong Yao ◽  
Muhammad Aslam Noor ◽  
Khalida Inayat Noor ◽  
Yeong-Cheng Liou ◽  
Huma Yaqoob
Keyword(s):  
Variational Inequalities ◽  
Banach Spaces ◽  
Extragradient Methods ◽  
System Of Variational Inequalities

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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