Some convergence properties of a method of multipliers for linearly constrained monotone variational inequalities

1998 ◽  
Vol 23 (3-5) ◽  
pp. 151-161 ◽  
Author(s):  
Bingsheng He ◽  
Hai Yang
Keyword(s):  
Variational Inequalities ◽  
Method Of Multipliers ◽  
Monotone Variational Inequalities ◽  
Convergence Properties ◽  
Linearly Constrained

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.

scholarly journals On the Graph of Solution Mappings of Variational Inequalities Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-4
Author(s):  
Qi-Qing Song
Keyword(s):  
Variational Inequalities ◽  
Monotone Variational Inequalities

This paper shows the property of homeomorphism between the space of monotone variational inequalities problems and the graph of their solution mappings.

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