Abstract

Bregman distances play a key role in generalized versions of the proximal algorithm. This paper proposes a new characterization of Bregman distances in terms of their gradient and Hessian matrix. Thanks to this characterization, we obtain two results: all the so called self-proximal distances are Bregman, and all the induced proximal distances, under some regularity assumptions, are Bregman functions

Author information

Contact details are reproduced from the original publication and may be historical.

Felipe Alvarez

Centro de Modelamiento Matemático, Dep. de Ingeniería Matemática, Universidad de Chile, Beauchef 851, Santiago, Chile
and: CNRS UMI 2807

Rafael Correa

Centro de Modelamiento Matemático, Dep. de Ingeniería Matemática, Universidad de Chile, Beauchef 851, Santiago, Chile

Matthieu Marechal

Instituto de Ciencias Basicas, Facultad de Ingeniería, Universidad Diego Portales, Ejército 441, Santiago, Chile

matthieu.marechal@udp.cl

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Suggested citation

F. Alvarez, R. Correa, M. Marechal. “Regular Self-Proximal Distances are Bregman.” Journal of Convex Analysis 24 (2017), No. 1, 135–148. https://doi.org/10.68381/jca24011

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Published by Heldermann Verlag, 2017. Rights now held by Banach Press.