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: | Xia Fu-Quan, Huang Nan-Jing |
Keywords: | projection algorithms, Hilbert space, inequality problems |
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.