Weak Convergence of the Operator Extrapolation Method for Variational Inequalities in Uniformly Convex Banach Spaces

Abstract

This work is devoted to the study of new iterative algorithms for solving variational inequalities in uniformly convex Banach spaces. The first algorithm is a modification of the forward-reflectedbackward algorithm, which uses the Alber generalized projection instead of the metric one. The second algorithm is an adaptive version of the first one, where the monotone step size update rule is used, which does not require knowledge of Lipschitz constants and linear search procedure.