An inertial subgradient extragradient method with Armijo type step size for pseudomonotone variational inequalities with non-Lipschitz operators in Banach spaces

Abstract

In this paper, we study the pseudomonotone variational inequality problems with non-Lipschitz operators. We propose an inertial subgradient extragradient method with Halpern technique and Armijo type step size for approximating the solution of the problem in the framework of 2-uniformly convex real Banach spaces. We prove that the sequence generated by our proposed method converges strongly to the solution of the problem under some mild conditions and without the weak sequential continuity condition often assumed by authors in solving pseudomonotone variational inequality problems. Finally, we provide some numerical experiments for the proposed method in comparison with other existing methods in the literature. Our result extends and improves several of the existing results in the current literature in this direction.