A New Inertial Subgradient Extragradient method for Solving Quasimonotone Variational Inequalities

The main aim of this paper is to study the numerical solution of variational inequalities involving quasimonotone operators in infinite-dimensional real Hilbert spaces. We prove that the iterative sequence generated by the proposed algorithm for the solution of quasimonotone variational inequalities converges weakly to the solution. The main advantage of the proposed iterative scheme is that it employs an inertial scheme and a monotone stepsize rule based on operator knowledge rather than a Lipschitz constant or another line search method. Numerical results show that the proposed algorithm is effective for solving quasimonotone variational inequalities.?