A Proximal Point Method for the Variational Inequality Problem in Banach Spaces

In this paper we prove well-definedness and weak convergence of the generalized proximal point method when applied to the variational inequality problem in reflexive Banach spaces. The proximal version we consider makes use of Bregman functions, whose original definition for finite dimensional space...

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Bibliographic Details
Published inSIAM journal on control and optimization Vol. 39; no. 5; pp. 1633 - 1649
Main Authors Burachik, Regina Sandra, Scheimberg, Susana
Format Journal Article
LanguageEnglish
Published Philadelphia Society for Industrial and Applied Mathematics 01.01.2000
Subjects
Algorithms
Banach spaces
Hilbert space
Optimization
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Summary:In this paper we prove well-definedness and weak convergence of the generalized proximal point method when applied to the variational inequality problem in reflexive Banach spaces. The proximal version we consider makes use of Bregman functions, whose original definition for finite dimensional spaces has here been properly extended to our more general framework.
ISSN:0363-0129
1095-7138
DOI:10.1137/S0363012998339745