  We introduce and study the convergence properties of a projection-type
algorithm for solving the variational inequality problem for point-to-set
operators. No monotoni\-city assumption is used in our analysis. The operator
defining the problem is only assumed to be continuous in the point-to-set
sense, i.e., inner- and outer-semicontinuous. Additionally, we assume
non-emptiness of the so-called dual solution set. We prove that the whole
sequence of iterates converges to a solution of the variational inequality.
Moreover, we provide numerical experiments illustrating the behavior of our
iterates. Through several examples, we provide a comparison with a recent
similar algorithm.
