An Accelerated Subgradient Extragradient Algorithm for Strongly Pseudomonotone Variational Inequality Problems

Jamilu Abubakar, Kamonrat Sombut, Habib ur Rehman, Abdulkarim Hassan Ibrahim

Abstract

In this article, we propose an accelerated subgradient extragradient algorithm for solving variational inequality problems involving strongly pseudomonotone operator by introducing an inertial extrapolation step with time variable step size. The scheme uses a non-summable and diminishing step size without the prior knowledge of the modulus of strong monotonicity and the lipschitz constant of the underlying operator. Furthermore, we prove the strong convergence of a sequence generated by the proposed algorithm to a solution of the problems under mild assumptions. We give numerical experiments to illustrate the inertial - effect and the computational performance of our proposed algorithm in comparison with the existing state of the art algorithms.