Numerical approach to monotone variational inequalities by a one-step projected reflected gradient method with line-search procedure

In this paper we revisit a recent approach to classical monotone variational inequalities by means of a projected reflected gradient-type method in RNRN. A line-search procedure is incorporated for possible varying step-sizes and no Lipschitz-continuity condition on the operator is required. A main feature of the proposed method is that it requires only one projection step onto the feasible set at each iteration.