A strong convergence theorem for Tseng’s extragradient method for solving variational inequality problems

Abstract

In this paper, we introduce a new algorithm for solving variational inequality problems with monotone and Lipschitz-continuous mappings in real Hilbert spaces. Our algorithm requires only to compute one projection onto the feasible set per iteration. We prove under certain mild assumptions, a strong convergence theorem for the proposed algorithm to a solution of a variational inequality problem. Finally, we give some numerical experiments illustrating the performance of the proposed algorithm for variational inequality problems.