Halpern subgradient extragradient algorithm for solving quasimonotone variational inequality problems

In this paper, we study the numerical solution of the variational inequalities involving quasi monotone operators in infinite-dimensional Hilbert spaces. We prove that the iterative sequence generated by the proposed algorithm for the solution of quasimonotone variational inequalities converges strongly to a solution. The main advantage of the proposed iterative schemes is that it uses a monotone and non-monotone step size rule based on operator knowledge rather than its Lipschitz constant or some other line search method.