Novel inertial extragradient method for solving pseudomonotone variational inequality problems

In this work, we revisit a version of the Tseng extragradient method for pseudomonotone variational inequalities and give sufficient conditions for its convergence. We first study a modified inertial Tseng method for variational inequalities to obtain weak convergence results under pseudomonotonicity and Lipschitz continuity assumptions. The advantage of the proposed method is that the inertial factor is chosen in [0,1]. Second, linear convergence is obtained for the proposed method under strong pseudomonotonicity and Lipschitz continuity assumptions. The main results obtained in this paper extend and improve some related works in the literature.