Directional end of a convex set: theory and applications.
type: Item
instance of: scholarly article
title: Directional end of a convex set: theory and applications.
zbMATH Open document ID: 1041.90058
DOI: 10.1023/A:1017583514580
published in: Journal of Optimization Theory and Applications
publication date: 2002-08-12T00:00:00Z
review text: The end of a nonempty convex set \(C\) in a given direction u (directional end) consists of all those points for which u is not a feasible direction with respect to \(C\). The authors discuss the properties of the directional end of general (closed) convex sets: its relation to quasipolyhedral sets and to the facial structure of \(C\), the characterizations of the extreme points and the full-dimensionality of \(C\) as well as its connection to the illumination of closed convex sets. Finally, these results are applied to the feasible set of an infinite linear inequality system.
reviewed by: Jan-Joachim Rückmann
Mathematics Subject Classification ID: 90C34
Mathematics Subject Classification ID: 52A20
zbMATH DE Number: 1779070
zbMATH Keywords: convex sets
zbMATH Keywords: linear systems
zbMATH Keywords: illumination
zbMATH Keywords: visibility
zbMATH Keywords: semi-infinite programming
author: Miguel Angel Goberna
author: Valentín Jornet
author: Margarita M. L. Rodríguez
MaRDI profile type: Publication
cites work: Cone convexity, cone extreme points, and nondominated solutions in decision problems with multiobjectives
cites work: Combinatorial problems on the illumination of convex bodies
cites work: Q4291359
cites work: Some characterizations of convex polyhedra
cites work: A Lipschitzian Characterization of Convex Polyhedra
cites work: Étude geométrique des espaces vectoriels II: Polyedres et polytopes convexes
cites work: Locally polyhedral linear inequality systems
cites work: Simplex-like trajectories on quasi-polyhedral sets.
cites work: Q4357206
cites work: Convex Analysis
cites work: Q4747150
cites work: Locally Farkas-Minkowski linear inequality systems
full work available at URL: a:1017583514580
OpenAlex ID: W1561280018
description: scientific article; zbMATH DE number 1779070