Reduntant axioms in the definitionof Bregman functions

Dan Butnariu (dbutnarumath.haifa.ac.il)
Charles Byrne (Charles_Byrneuml.edu)
Yair Censor (yairmath.haifa.ac.il)

Abstract: The definition of a Bregman function, given by Censor and Lent in 1981 on the basis of Bregman's seminal 1967 paper, was subsequently used in a plethora of research works as a tool for building sequential and inherently parallel feasibility and optimization algorithms. Solodov and Svaiter have recently shown that it is not

Keywords: Bregman function, Bregman distance, Kullback-Leibler distance, modulus of total convexity, sequential consistency, totally convex function.

Category 1: Nonlinear Optimization (Constrained Nonlinear Optimization )

Citation: Journal of Convex Analysis, Vol. 10 (2003), pp. 245-254.

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Entry Submitted: 03/17/2002
Entry Accepted: 03/17/2002
Entry Last Modified: 10/04/2004

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