A NEW HYBRID GRADIENT PROJECTION METHOD FOR THE PSEUDOMONOTONE VARIATIONAL INEQUALITY AND FIXED POINT PROBLEM IN BANACH SPACE

Tóm tắt

It is known that the variational inequality problem is an extension of the nonlinear compensation problem. It includes convex optimization problems, game theory, Kakutani fixed-point problems, polynomial and tensor variational inequalities, and direct applications in many fields such as operations research, Nash-Counot equilibrium model, and transportation. Methods for solving variational inequalities and fixed points problems have received much attention. However, most of recent methods for solving variational inequalities and fixed points problems require the monotone and Lipschitz continuous or inversestrongly monotone assumptions of the cost mapping. Algorithms are mainly built on finite dimensional spaces or Hilbert spaces. In this paper, we propose a new hybrid gradient projection method to find a common element of the solution set of pseudo-monotone, Lipschitz continuous variational inequality problem with the fixed point set of relatively weak non-expansion mapping in Banach spaces. With the given assumptions, we obtain a strong convergence theorem of the algorithm.