On the union of closed balls property
type: Item
instance of: scholarly article
title: On the union of closed balls property
zbMATH Open document ID: 1262.49018
author: Chadi Nour
author: Jean Takche
published in: Journal of Optimization Theory and Applications
publication date: 2013-02-14T00:00:00Z
review text: The authors propose in this paper a new analytical proof for a strengthened version of the variable radius form of the union of closed balls conjecture introduced by the same authors in an old paper. The improvement results from the fact that they provide a bigger radius for the balls covering the given closed set. The main keys of the proof are the new analytical characterizations of the \(\psi\)-union of closed balls property and the \(\theta\)-exterior sphere condition together with some techniques from nonsmooth analysis. As a corollary, the authors deduce a new analytical proof for the weak version of the union of closed balls conjecture. They also introduce a strong version of the variable radius form of this conjecture and prove, by a counterexample, that the geometric methods used in the old paper to deduce the variable radius form from the constant radius one, do not work in the strong case.
Mathematics Subject Classification ID: 49J52
Mathematics Subject Classification ID: 49N60
zbMATH DE Number: 6136278
zbMATH Keywords: exterior and interior sphere conditions
zbMATH Keywords: union of closed balls property
zbMATH Keywords: proximal analysis
zbMATH Keywords: nonsmooth analysis
reviewed by: Vasile Iftode
MaRDI profile type: Publication
full work available at URL: s10957-012-0068-8
OpenAlex ID: W2069433503
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DOI: 10.1007/S10957-012-0068-8
description: scientific article; zbMATH DE number 6136278