New extragradient-type methods for general variational inequalities

Some Extragradient Methods for Nonconvex Quasi Variational Inequalities (communicated by M.s.moslehian)

In this paper, we introduce and consider a new class of variational inequalities involving two operators, which is called the general nonconvex quasi variational inequality. Several special cases are discussed. We use the projection technique to establish the equivalence between the general nonconvex quasi variational inequalities and the fixed point problems. This alternative equivalent formul...

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...

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

Operator-splitting Methods for General Mixed Variational Inequalities

In this paper, we use the technique of updating the solution to suggest and analyze a class of new splitting methods for solving general variational inequalities. It is shown that these modified methods converge for pseudomonotone operators, which is a weaker condition than monotonicity. Our method includes the two-step forward-backward splitting and extragradient methods for solving various cl...

Common solutions to pseudomonotone equilibrium problems

‎In this paper‎, ‎we propose two iterative methods for finding a common solution of a finite family of equilibrium problems ‎for pseudomonotone bifunctions‎. ‎The first is a parallel hybrid extragradient-cutting algorithm which is extended from the‎ ‎previously known one for variational inequalities to equilibrium problems‎. ‎The second is a new cyclic hybrid‎ ‎extragradient-cutting algorithm‎....