AN HYBRID EXTRAGRADIENT ALGORITHM FOR VARIATIONAL INEQUALITIES WITH PSEUDOMONOTONE EQUILIBRIUM CONSTRAINTS - Dinh, B. V. (Journal of Nonlinear Analysis and Optimization: Theory & Applications (JNAO), 2018)
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.