An effective iterative projection method for variational inequalities in Hilbert spaces

Abstract

In this paper, a projection-type method is proposed for solving a variational inequality problem involving a monotone and Lipschitz continuous operator in a Hilbert space. One only projection in the method is used per each iteration. The strong convergence of iterative sequences generated by the method is established under suitable conditions imposed on control parameters. The analysis is based on the regularization technique. Numerical experiments comparing the proposed method with some existing methods are given.