An inertial Popov's method for solving pseudomonotone variational inequalities

Abstract

In this work, we propose a new modified Popov's method by using inertial effect for solving the variational inequality problem in real Hilbert spaces. The advantage of the proposed algorithm is the computation of only one value of the inequality mapping and one projection onto the admissible set per one iteration as well as it does not need to the prior knowledge of the Lipschitz constants of the variational inequality mapping. We present weak convergence theorem of the proposed algorithm under pseudomonotonicity and Lipschitz continuity of the associated mapping. Our results generalize and extend some related results in the literature and primary numerical experiments demonstrate the applicability of the scheme.