A new extragradient-like method for solving variational inequality problems

A New Version of Extragradient Method for Variational Inequality Problems

In this paper, we propose a new version of extragradient method for the variational inequality problem. The method uses a new searching direction which differs from any one in existing projection-type methods, and is of a better stepsize rule. Under a certain generalized monotonicity condition, it is proved to be globally convergent. @ 2001 Eisevier Science Ltd. All rights reserved. Keywords-Vs...

An extragradient-like approximation method for variational inequality problems and fixed point problems

The purpose of this paper is to investigate the problem of finding a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of a variational inequality problem for a monotone, Lipschitz continuous mapping. We introduce an extragradient-like approximation method which is based on so-called extragradient method and viscosity approximation method. We establish...

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...

Research Article An Extragradient Method for Fixed Point Problems and Variational Inequality Problems

A modified subgradient extragradient method for solving monotone variational inequalities

In the setting of Hilbert space, a modified subgradient extragradient method is proposed for solving Lipschitz-continuous and monotone variational inequalities defined on a level set of a convex function. Our iterative process is relaxed and self-adaptive, that is, in each iteration, calculating two metric projections onto some half-spaces containing the domain is involved only and the step siz...