A Projection‐Proximal Point Algorithm for Solving Generalized Variational Inequalities

A Projection‐Proximal Point Algorithm for Solving Generalized Variational Inequalities

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Article ID: iaor20116443
Volume: 150
Issue: 1
Start Page Number: 98
End Page Number: 117
Publication Date: Jul 2011
Journal: Journal of Optimization Theory and Applications
Authors: ,
Keywords: projection algorithms, Hilbert space, inequality problems
Abstract:

In this paper, a projection‐proximal point method for solving a class of generalized variational inequalities is considered in Hilbert spaces. We investigate a general iterative algorithm, which consists of an inexact proximal point step followed by a suitable orthogonal projection onto a hyperplane. We prove the convergence of the algorithm for a pseudomonotone mapping with weakly upper semicontinuity and weakly compact and convex values. We also analyze the convergence rate of the iterative sequence under some suitable conditions.

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