An inexact hybrid projection-proximal point algorithm for solving generalized mixed variational inequalities

In this paper, we investigate an inexact hybrid projection-proximal method for solving a class of generalized mixed variational inequalities in Hilbert spaces. We construct a general inexact hybrid projection-proximal point algorithm, in which an inexact relaxed proximal point step is followed by a suitable orthogonal projection onto a hyperplane. Under some suitable conditions concerned with the pseudomonotone set-valued mapping T, the nonsmooth convex function f and the step size λ_k, we prove the convergence of the inexact hybrid projection-proximal point algorithm for solving generalized mixed variational inequalities in Hilbert spaces.