AN HYBRID EXTRAGRADIENT ALGORITHM FOR VARIATIONAL INEQUALITIES WITH PSEUDOMONOTONE EQUILIBRIUM CONSTRAINTS

BUI VAN  DINH

AN HYBRID EXTRAGRADIENT ALGORITHM FOR VARIATIONAL INEQUALITIES WITH PSEUDOMONOTONE EQUILIBRIUM CONSTRAINTS

Authors

BUI VAN DINH Department of Mathematics, Faculty of Information Technology, Le Quy Don Technical University, Hanoi, Vietnam

Keywords:

Variational inequalities, equilibrium problems, KyFan inequality, auxiliary subproblem principle, projection method, Armijo linesearch, pseudomonotone

Abstract

In this paper, we propose a new hybrid extragradient algorithm for solving a variational inequality problem over the solution set of an equilibrium problem in Euclidean space . By using fixed point and hybrid plane cutting techniques, we show that this problem can be solved by an explicit extragradient method. Under certain conditions on parameters, the convergence of the iteration sequences generated by the algorithm are obtained.