A MODIFIED GRADIENT PROJECTION ALGORITHM FOR VARIATIONAL INEQUALITIES AND RELATIVELY NONEXPANSIVE MAPPINGS IN BANACH SPACES

Abstract

In this paper, we modify the gradient projection algorithm proposed by [K. Nakajo, Strong convergence for gradient projection method and relatively nonexpansive mappings in Banach spaces, Applied Mathematics and Computation, 271 (2015), 251-258] for solving a variational inequality problem involving a monotone and Lipschitz continuous mapping and a fixed point problem of a relatively nonexpansive mapping in Banach spaces. The purpose of this modification is to replace a projection onto a general closed convex set to one projection onto a half-space. The latter projection (onto a halfspace) is easier to compute. We prove the iteration sequence generated by this method is weak convergence.