Inertial extragradient algorithms with non-monotone stepsizes for pseudomonotone variational inequalities and applications

Abstract

The goal of this paper is to construct several fast iterative algorithms for solving pseudomonotone variational inequalities in real Hilbert spaces. We introduce two extragradient algorithms with inertial terms and give a strong convergence analysis under suitable assumptions. The suggested algorithms need to compute the projection on the feasible set only once in each iteration and can update the step size adaptively without any line search condition. Some numerical experiments and applications are implemented to illustrate the advantages and efficiency of the suggested algorithms over the related known methods.