Upper and lower bounds for the Bregman divergence

In this paper we study upper and lower bounds on the Bregman divergence [Formula: see text] for some convex functional [Formula: see text] on a normed space [Formula: see text] , with subgradient [Formula: see text] . We give a considerably simpler new proof of the inequalities by Xu and Roach for t...

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Detalles Bibliográficos
Autor principal: Sprung, Benjamin
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2019
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6325099/
https://www.ncbi.nlm.nih.gov/pubmed/30839886
http://dx.doi.org/10.1186/s13660-018-1953-y
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author Sprung, Benjamin
author_facet Sprung, Benjamin
author_sort Sprung, Benjamin
collection PubMed
description In this paper we study upper and lower bounds on the Bregman divergence [Formula: see text] for some convex functional [Formula: see text] on a normed space [Formula: see text] , with subgradient [Formula: see text] . We give a considerably simpler new proof of the inequalities by Xu and Roach for the special case [Formula: see text] , [Formula: see text] . The results can be transferred to more general functions as well.
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spelling pubmed-63250992019-01-23 Upper and lower bounds for the Bregman divergence Sprung, Benjamin J Inequal Appl Research In this paper we study upper and lower bounds on the Bregman divergence [Formula: see text] for some convex functional [Formula: see text] on a normed space [Formula: see text] , with subgradient [Formula: see text] . We give a considerably simpler new proof of the inequalities by Xu and Roach for the special case [Formula: see text] , [Formula: see text] . The results can be transferred to more general functions as well. Springer International Publishing 2019-01-08 2019 /pmc/articles/PMC6325099/ /pubmed/30839886 http://dx.doi.org/10.1186/s13660-018-1953-y Text en © The Author(s) 2019 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Research
Sprung, Benjamin
Upper and lower bounds for the Bregman divergence
title Upper and lower bounds for the Bregman divergence
title_full Upper and lower bounds for the Bregman divergence
title_fullStr Upper and lower bounds for the Bregman divergence
title_full_unstemmed Upper and lower bounds for the Bregman divergence
title_short Upper and lower bounds for the Bregman divergence
title_sort upper and lower bounds for the bregman divergence
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6325099/
https://www.ncbi.nlm.nih.gov/pubmed/30839886
http://dx.doi.org/10.1186/s13660-018-1953-y
work_keys_str_mv AT sprungbenjamin upperandlowerboundsforthebregmandivergence

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