Revisiting subgradient extragradient methods for solving variational inequalities

Abstract

In this paper, several extragradient algorithms with inertial effects and adaptive non-monotonic step sizes are proposed to solve pseudomonotone variational inequalities in real Hilbert spaces. The strong convergence of the proposed methods is established without the prior knowledge of the Lipschitz constant of the mapping. Some numerical experiments are given to illustrate the advantages and efficiency of the proposed schemes over previously known ones.