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An Inexact Proximal Algorithm for Pseudomonotone and Quasimonotone Variational Inequalities

Erik Papa Quiroz (erikpapa***at***gmail.com)
Lennin Mallma Ramirez (lenninmr***at***gmail.com)
Paulo Roberto Oliveira (poliveir***at***cos.ufrj.br)

Abstract: In this paper we introduce an inexact proximal point algorithm using proximal distances for solving variational inequality problems when the mapping is pseudomonotone or quasimonotone. Under some natural assumptions we prove that the sequence generates by the algorithm is convergent for the pseudomonotone case and weakly convergent for the quasimonotone ones. This approach unifies the results obtained by Auslender, Teboulle and Ben-Tiba (1999), Brito et al. (2012) and extends the convergence properties for the class of divergence distances and Bregman distances.

Keywords: Variational inequalities, proximal distance, proximal point algorithm, quasimonotone and pseudomonotone mapping

Category 1: Convex and Nonsmooth Optimization (Nonsmooth Optimization )


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Entry Submitted: 05/15/2015
Entry Accepted: 05/15/2015
Entry Last Modified: 05/19/2015

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