Self-adaptive inertial subgradient extragradient scheme for pseudomonotone variational inequality problem
Jamilu Abubakar, Poom Kumam, Habib ur Rehman · International Journal of Nonlinear Sciences and Numerical Simulation · 2021
Abstract In this article, we propose a self-adaptive inertial subgradient extragradient algorithm for solving variational inequality problems involving pseudomonotone operator. The scheme uses a variable step sizes and inertial extrapolation step. The step size is self-adaptive, which does not require the prior knowledge of the Lipschitz constant of the underlying operator. Furthermore, under mild assumptions, we prove the weak convergence of the sequence generated by the proposed algorithm to a solution of the considered problem. 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.