A relaxed version of the gradient projection method for variational inequalities with applications

Abstract

In this paper, we propose a relaxed version of gradient projection method for strongly monotone variational inequalities defined on a level set of a (possibly non-differentiable) convex function. Our algorithms can be implemented easily since it computes on every iteration one projection onto some half-space containing the feasible set and only one value of the underlying mapping. Under mild and standard conditions we establish the strong convergence of the proposed algorithm. The performance is presented through a numerical example in solving the image deblurring problem and compare this algorithm with other algorithms in the literature.