Bregman distances and Klee sets

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dc.creatorBauschke, Heinz H.
dc.creatorWang, Xianfu
dc.creatorYe, Jane
dc.creatorYuan, Xiaoming
dc.date2008-02-16
dc.date.accessioned2026-07-07T09:21:25Z
dc.date.available2026-07-07T09:21:25Z
dc.descriptionIn 1960, Klee showed that a subset of a Euclidean space must be a singleton provided that each point in the space has a unique farthest point in the set. This classical result has received much attention; in fact, the Hilbert space version is a famous open problem. In this paper, we consider Klee sets from a new perspective. Rather than measuring distance induced by a norm, we focus on the case when distance is meant in the sense of Bregman, i.e., induced by a convex function. When the convex function has sufficiently nice properties, then - analogously to the Euclidean distance case - every Klee set must be a singleton. We provide two proofs of this result, based on Monotone Operator Theory and on Nonsmooth Analysis. The latter approach leads to results that complement work by Hiriart-Urruty on the Euclidean case.
dc.identifierhttps://arxiv.org/abs/0802.2322
dc.identifierhttp://arxiv.org/abs/0802.2322
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/155014
dc.subjectFunctional Analysis
dc.subjectOptimization and Control
dc.subject47H05; 41A65; 49J52
dc.titleBregman distances and Klee sets
dc.typetext

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