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

Authors:
Fu-quan Xia;Nan-jing Huang
Affiliations:
Department of Mathematics, Sichuan Normal University, Chengdu, Sichuan 610066, PR China;Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, PR China
Venue:
Computers & Mathematics with Applications
Year:
2011

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Abstract

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 @l"k, we prove the convergence of the inexact hybrid projection-proximal point algorithm for solving generalized mixed variational inequalities in Hilbert spaces.