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 TT, the nonsmooth convex function ff and the step size λkλk, we prove the convergence of the inexact hybrid projection–proximal point algorithm for solving generalized mixed variational inequalities in Hilbert spaces.