Strong Convergence of a Double Projection-type Method for Monotone Variational Inequalities in Hilbert Spaces

Abstract

We introduce a projection-type algorithm for solving monotone variational inequality problems in real Hilbert spaces. We prove that the whole sequence of iterates converges strongly to a solution of the variational inequality. The method uses only two projections onto the feasible set in each iteration in contrast to other c algorithms which either require plenty of projections within a stepsize rule or have to compute projections on possibly more complicated sets. Some numerical results illustrate the practical behaviour of our method.