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On Bregman-type distances for convex functions and maximally monotone operators
Burachik, Regina S. (University of South Australia. School of Information Technology and Mathematical Sciences)
Martínez-Legaz, Juan Enrique (Universitat Autònoma de Barcelona. Departament d'Economia i d'Història Econòmica)

Date: 2018
Abstract: Given two point to set operators, one of which is maximally monotone, we introduce a new distance in their graphs. This new concept reduces to the classical Bregman distance when both operators are the gradient of a convex function. We study the properties of this new distance and establish its continuity properties. We derive its formula for some particular cases, including the case in which both operators are linear monotone and continuous. We also characterize all bi-functions D for which there exists a convex function h such that D is the Bregman distance induced by h.
Note: Número d'acord de subvenció MINECO/MTM2014-59179- C2-2-P
Note: Número d'acord de subvenció MINECO/SEV-2015-0563
Rights: Tots els drets reservats
Language: Anglès.
Document: article ; recerca ; acceptedVersion
Subject: Maximally monotone operators ; Bregman distances ; Banach spaces ; Representable operators ; Fitzpatrick functions ; Convex functions ; Variational inequalities
Published in: Set-Valued and Variational Analysis, Vol. 26, Núm. 2 (2018) , p. 369-384, ISSN 1877-0541

DOI: 10.1007/s11228-017-0443-6


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 Record created 2018-11-06, last modified 2019-07-03



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