A modified extragradient method for multi-valued variational inequality problems

Abstract

In this paper, we consider a class of multi-valued variational inequality problems in which the involving function is continuous and pseudomonotone. This problem has a broad applications in equilibrium and optimization. In order to reduce the computation, we present a modified extragradient algorithm for solving multi-valued variational inequalities in which each iteration is obtained as the projection onto the intersection of the feasible set and the hyperplane containing the solution set. Moreover, we prove the sequence generated by the proposed algorithm is globally convergence with requiring the involving function being continuous and pseudomonitone on the feasible set. Finally, we give several numerical experiments to demonstrate the efficiency of the proposed algorithm.