A New Inertial Subgradient Extragradient Method for Solving Quasimonotone Variational Inequalities

Habib ur Rehman, Wiyada Kumam, Kamonrat Sombut

Abstract

The main aim of this paper is to investigate the numerical solution of variational inequalities involving quasi-monotone operators in infinite-dimensional real Hilbert spaces. We prove that the iterative sequence generated by the proposed algorithm for the solution of quasi-monotone variational inequalities converges weakly towards a solution. The main advantages of the proposed iterative scheme are that it uses an inertial scheme and a monotone step size rule based on operator knowledge rather than a Lipschitz constant or another line search method. Numerical results show that the proposed algorithm is useful to solve quasi-monotone variational inequalities.