A characterization of Bregman firmly nonexpansive operators using a new monotonicity concept

Title: A characterization of Bregman firmly nonexpansive operators using a new monotonicity concept
Creator: Borwein, Jonathan M.; Reich, Simeon; Sabach, Shoham
Relation: Journal of Nonlinear and Convex Analysis Vol. 12, Issue 1, p. 161-184
Relation: http://www.ybook.co.jp/online2/opjnca/vol12/p161.html
Publisher: Yokohama Publishers
Resource Type: journal article
Date: 2011
Description: The property of nonexpansivity (1-Lipschitz) is very important in the analysis of many optimization problems. In this paper we study a more general notion of nonexpansivity - Bregman nonexpansivity. We present a characterization of Bregman firmly nonexpansive operators in general reflexive Banach spaces. This characterization allows us to construct Bregman firmly nonexpansive operators explicitly. We provide several examples of such operators with respect to the Boltzmann-Shannon entropy and the Fermi-Dirac entropy in Euclidean spaces. We also compute resolvents with respect to these functions.
Subject: Boltzmann-Shannon entropy; Bregman distance; Bregman firmly nonexpansive operator; Fermi Dirac entropy; nonexpansive operator; monotone mapping; resolvent; T monotone mapping; totally convex function
Identifier: http://hdl.handle.net/1959.13/1046907
Identifier: uon:14703
Identifier: ISSN:1345-4773
Language: eng
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