Characterizing sets of lower bounds: a hidden convexity result
type: Item
instance of: scholarly article
title: Characterizing sets of lower bounds: a hidden convexity result
zbMATH Open document ID: 1391.52001
author: E. Ernst
author: Alberto Zaffaroni
published in: Set-Valued and Variational Analysis
publication date: 2018-02-06T00:00:00Z
full work available at URL: http://hdl.handle.net/11380/1139160
review text: The authors look for description of the set of lower bounds of a subset in an ordered vector space. Clearly, such a set \(C\) enjoys the following properties: (1) \(C\) is downward; (2) \(C\) is upper bounded; (3) \(C\) contains the supremum of its every subset that admits one. These conditions are proved to be sufficient in the case of a finite-dimensional space and a polyhedral positive cone. Simple counter-examples demonstrate the failure of the sufficiency in absence of polyhedrality.
Mathematics Subject Classification ID: 52A07
Mathematics Subject Classification ID: 46A55
zbMATH DE Number: 6834679
zbMATH Keywords: partially ordered vector spaces
zbMATH Keywords: polyhedral cone
zbMATH Keywords: set of lower bounds
reviewed by: S. S. Kutateladze
MaRDI profile type: Publication
OpenAlex ID: W2618213242
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DOI: 10.1007/S11228-017-0416-9
description: scientific article; zbMATH DE number 6834679