Closed convex sets of Minkowski type

In this paper we provide several characterizations of Minkowski sets, i.e. closed, possibly unbounded, convex sets which are representable as the convex hulls of their sets of extreme points. The equality between the relative boundary of a closed convex set containing no lines and its Pareto-like as...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2016-12, Vol.444 (2), p.1195-1202
Main Authors: Martínez-Legaz, J.E., Pintea, Cornel
Format: Article
Language:English
Subjects:
Closed convex sets
Extreme points
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Summary:In this paper we provide several characterizations of Minkowski sets, i.e. closed, possibly unbounded, convex sets which are representable as the convex hulls of their sets of extreme points. The equality between the relative boundary of a closed convex set containing no lines and its Pareto-like associated set ensures the Minkowski property of the set. In two dimensions this equality characterizes the Minkowski sets containing no lines.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2016.06.073