Projected reflected gradient method with momentum terms for variational inequalities

In this paper, we propose a projected reflected gradient method with momentum terms for solving variational inequality problems in Hilbert spaces. The proposed method involves only one projection onto the feasible set and one operator evaluation per iteration. Under certain standard assumptions, we establish the weak convergence of the proposed method. Furthermore, we also establish the linear convergence result when the operator is strongly monotone and Lipschitz continuous. Finally, we present numerical experiments to show that the projected reflected gradient method with momentum terms outperforms some related methods in the literature for solving variational inequality problems.