An alternated inertial method for pseudomonotone variational inequalities in Hilbert spaces

Abstract

In this paper, we introduce a new relaxed extrgadient algorithm with alternated inertial extrapolation step and self adaptive variable stepsizes for solving variational inequality problems whose cost operator is pseudomonotone operator in Hilbert spaces. We establish the weak convergence of the proposed algorithm and linear convergence under some standard assumptions. Numerical experiments are given to support theoretical results and comparison with recent related methods.