A strong convergence theorem for solving variational inequality problems with pseudo-monotone and Lipschitz mappings

In this paper, we propose a Mann-type self-adaptive projected reflected subgradient extragradient algorithm for solving the classical variational inequality problem with Lipschitz continuous and pseudo-monotone mappings in a real Hilbert space.The strong convergence of the proposed algorithm is proven without the prior knowledge of the Lipschitz constant of the cost function.Finally, we give some numerical examples to illustrate the superiority of our proposed algorithm.