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A Projection-Proximal Point Algorithm for Solving Generalized Variational Inequalities

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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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Authors and Affiliations

  1. Department of Mathematics, Sichuan Normal University, Chengdu, Sichuan, 610066, China

    Fu-Quan Xia

  2. Department of Mathematics, Sichuan University, Chengdu, Sichuan, 610064, China

    Nan-Jing Huang

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  1. Fu-Quan Xia
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  2. Nan-Jing Huang
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Correspondence to Nan-Jing Huang.

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Xia, FQ., Huang, NJ. A Projection-Proximal Point Algorithm for Solving Generalized Variational Inequalities. J Optim Theory Appl 150, 98–117 (2011). https://doi.org/10.1007/s10957-011-9825-3

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  • DOI: https://doi.org/10.1007/s10957-011-9825-3

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