The Penalty Method for a New System of Generalized Variational Inequalities

An Iterative Scheme for Generalized Equilibrium, Variational Inequality and Fixed Point Problems Based on the Extragradient Method

The problem ofgeneralized equilibrium problem is very general in the different subjects .Optimization problems, variational inequalities, Nash equilibrium problem and minimax problems are as special cases of generalized equilibrium problem. The purpose of this paper is to investigate the problem of approximating a common element of the set of generalized equilibrium problem, variational inequal...

ψ-pseudomonotone generalized strong vector variational inequalities with application

In this paper, we establish an existence result of the solution for an generalized strong vector variational inequality already considered in the literature and as applications we obtain a new coincidence point theorem in Hilbert spaces.    

An inexact alternating direction method with SQP regularization for the structured variational inequalities

In this paper, we propose an inexact alternating direction method with square quadratic proximal  (SQP) regularization for  the structured variational inequalities. The predictor is obtained via solving SQP system  approximately  under significantly  relaxed accuracy criterion  and the new iterate is computed directly by an explicit formula derived from the original SQP method. Under appropriat...

A Relaxed Extra Gradient Approximation Method of Two Inverse-Strongly Monotone Mappings for a General System of Variational Inequalities, Fixed Point and Equilibrium Problems

On nonlinear evolution variational inequalities involving variable exponent

In this paper, we discuss a class of quasilinear evolution variational inequalities with variable exponent growth conditions in a generalized Sobolev space. We obtain the existence of weak solutions by means of penalty method. Moreover, we study the extinction properties of weak solutions to parabolic inequalities and provide a sufficient condition that makes the weak solutions vanish in a fini...