Strong convergence of double-projection method for variational inequality problems

The paper proposes a numerical method for solving a variational inequality problem (VIP) involving a monotone and Lipschitz continuous operator in a Hilbert space. The method can be considered as a combination between an extragradient method and a regularization method. We prove that the iterative sequences generated by our method converge strongly to the smallest norm solution of problem VIP. Obtaining the strong convergence of the iterative sequences is based on regularization solutions when the regularization parameters are chosen suitably. Our numerical experiments are implemented to illustrate the behavior of the new method. The numerical results have shown the effectiveness and fast convergence of the method over existing methods.