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

Authors:
Regina Sandra Burachik;Susana Scheimberg
Affiliations:
-;-
Venue:
SIAM Journal on Control and Optimization
Year:
2000

Citing 0
Cited 4

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Pseudomonotone$${_{\ast}}$$ maps and the cutting plane property

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A modified extragradient method for inverse-monotone operators in Banach spaces

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Abstract

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.