Characterizations of evenly convex sets and evenly quasiconvex functions
type: Item
instance of: scholarly article
title: Characterizations of evenly convex sets and evenly quasiconvex functions
zbMATH Open document ID: 1019.52001
DOI: 10.1016/S0022-247X(02)00206-8
published in: Journal of Mathematical Analysis and Applications
publication date: 2003-02-11T00:00:00Z
review text: An evenly convex set \(K\) in a Banach space is the intersection of open half spaces. It is shown that this is equivalent to saying that for any closure point \(x\) of \(K\) not in \(K\), no translate through \(x\), of any linear subspace of the tangent cone at \(x\), meets \(K\). This yields a fully primal characterization of evenly quasiconvex functions on a separable Banach space (having evenly convex lower level sets), i.e. not referring to dual functionals and/or separation properties.
reviewed by: Frank Plastria
Mathematics Subject Classification ID: 52A07
Mathematics Subject Classification ID: 26B25
zbMATH DE Number: 1866597
zbMATH Keywords: evenly convex sets
zbMATH Keywords: evenly quasiconvex functions
Wikidata QID: Q57836405
author: A. Daniilidis
author: Juan-Enrique Martínez-Legaz
MaRDI profile type: Publication
cites work: Partially finite convex programming. I: Quasi relative interiors and duality theory
cites work: Q3325474
cites work: Q5814430
cites work: Q4040695
cites work: Nonlinear monotone operators with values in \({\mathcal L}(X,Y)\)
cites work: Hereditary order convexity in \({\mathcal L}(X,Y)\)
cites work: Q3670037
cites work: Quasiconvex duality theory by generalized conjugation methods
cites work: Duality between direct and indirect utility functions under minimal hypotheses
cites work: Conjugacy in quasi-convex programming
cites work: Q4869223
cites work: On Quasi-Convex Duality
cites work: Q4339231
description: scientific article; zbMATH DE number 1866597