A general descent framework for the monotone variational inequality problem

1993 ◽  
Vol 61 (1-3) ◽  
pp. 281-300 ◽  
Author(s):  
Jia Hao Wu ◽  
Michael Florian ◽  
Patrice Marcotte
Keyword(s):  
Variational Inequality ◽  
Variational Inequality Problem ◽  
Inequality Problem ◽  
Monotone Variational Inequality

scholarly journals On the $O(1/k)$ Convergence Rate of He's Alternating Directions Method for a Kind of Structured Variational Inequality Problem

2015 ◽  
Vol 7 (2) ◽  
pp. 69
Author(s):  
Haiwen Xu
Keyword(s):  
Variational Inequality ◽  
Convergence Rate ◽  
Variational Inequality Problem ◽  
Variational Inequality Problems ◽  
System Of Nonlinear Equations ◽  
Inequality Problem ◽  
Quadratic Minimization ◽  
Projection And Contraction Methods ◽  
Monotone Variational Inequality ◽  
Alternating Directions Method

The  alternating directions method for a kind of structured variational inequality problem (He, 2001) is an attractive method for structured monotone variational inequality problems. In each iteration, the subproblemsare  convex quadratic minimization problem with simple constraintsand a well-conditioned system of nonlinear equations that can be efficiently solvedusing classical methods. Researchers have recently described the convergence rateof projection and contraction methods for variational inequality problems andthe original ADM and its linearized variant. Motivated and inspired by researchinto the convergence rate of these methods, we provide a simple proof to show the $O(1/k)$ convergencerate of  alternating directions methods for structured monotone variational inequality problems (He, 2001).

scholarly journals Algorithms for Solving the Variational Inequality Problem over the Triple Hierarchical Problem

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Thanyarat Jitpeera ◽  
Poom Kumam
Keyword(s):  
Fixed Point ◽  
Variational Inequality ◽  
Nonexpansive Mapping ◽  
Strong Convergence ◽  
Variational Inequality Problem ◽  
Strong Convergence Theorem ◽  
Fixed Point Set ◽  
Inequality Problem ◽  
Point Set ◽  
Monotone Variational Inequality

This paper discusses the monotone variational inequality over the solution set of the variational inequality problem and the fixed point set of a nonexpansive mapping. The strong convergence theorem for the proposed algorithm to the solution is guaranteed under some suitable assumptions.

scholarly journals Topological degree and application to a parabolic variational inequality problem

2001 ◽  
Vol 25 (4) ◽  
pp. 273-287 ◽  
Author(s):  
A. Addou ◽  
B. Mermri
Keyword(s):  
Variational Inequality ◽  
Topological Degree ◽  
Variational Inequality Problem ◽  
Maximal Monotone ◽  
Maximal Monotone Operators ◽  
Monotone Operators ◽  
Parabolic Variational Inequality ◽  
Inequality Problem ◽  
Monotone Map ◽  
New Formulation

We are interested in constructing a topological degree for operators of the formF=L+A+S, whereLis a linear densely defined maximal monotone map,Ais a bounded maximal monotone operators, andSis a bounded demicontinuous map of class(S+)with respect to the domain ofL. By means of this topological degree we prove an existence result that will be applied to give a new formulation of a parabolic variational inequality problem.

scholarly journals A Mean Extragradient Method for Solving Variational Inequalities

Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 462
Author(s):  
Apichit Buakird ◽  
Nimit Nimana ◽  
Narin Petrot
Keyword(s):  
Hilbert Space ◽  
Variational Inequality ◽  
Weak Convergence ◽  
Numerical Experiments ◽  
Variational Inequality Problem ◽  
Extragradient Method ◽  
Mean Value ◽  
Inequality Problem ◽  
The Mean ◽  
Mean Value Method

We propose a modified extragradient method for solving the variational inequality problem in a Hilbert space. The method is a combination of the well-known subgradient extragradient with the Mann’s mean value method in which the updated iterate is picked in the convex hull of all previous iterates. We show weak convergence of the mean value iterate to a solution of the variational inequality problem, provided that a condition on the corresponding averaging matrix is fulfilled. Some numerical experiments are given to show the effectiveness of the obtained theoretical result.

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