A New Inertial Subgradient Extragradient Method for Solving Quasimonotone Variational Inequalities

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.