Abstract

In this paper, we introduce an explicit iterative algorithm for solving a (pseudo) monotone variational inequality under Lipschitz condition in a Hilbert space. The algorithm is constructed around some projections incorporated by inertial terms. It uses variable stepsizes which are generated at each iteration by some simple computations. Furthermore, it can be easily implemented without the prior knowledge of the Lipschitz constant of the operator. Theorems of weak convergence are established under mild conditions, and some numerical results are reported for the purpose of comparison with other algorithms. The obtained results in this paper extend some related works in the literature.