Closed convex sets of Minkowski type

J. E. Martínez-Legaz; Cornel Pintea

doi:10.1016/j.jmaa.2016.06.073

Closed convex sets of Minkowski type

J. E. Martínez-Legaz, Cornel Pintea

Department of Economics and Economic History

Research output: Contribution to journal › Article › Research › peer-review

1 Citation (Scopus)

Abstract

© 2016 Elsevier Inc. 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.

Original language	English
Pages (from-to)	1195-1202
Journal	Journal of Mathematical Analysis and Applications
Volume	444
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2016.06.073
Publication status	Published - 15 Dec 2016

Keywords

Closed convex sets
Extreme points

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10.1016/j.jmaa.2016.06.073

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title = "Closed convex sets of Minkowski type",

abstract = "{\textcopyright} 2016 Elsevier Inc. 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.",

keywords = "Closed convex sets, Extreme points",

author = "Mart{\'i}nez-Legaz, {J. E.} and Cornel Pintea",

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T1 - Closed convex sets of Minkowski type

AU - Martínez-Legaz, J. E.

AU - Pintea, Cornel

PY - 2016/12/15

Y1 - 2016/12/15

N2 - © 2016 Elsevier Inc. 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.

AB - © 2016 Elsevier Inc. 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.

KW - Closed convex sets

KW - Extreme points

U2 - 10.1016/j.jmaa.2016.06.073

DO - 10.1016/j.jmaa.2016.06.073

M3 - Article

SN - 0022-247X

VL - 444

SP - 1195

EP - 1202

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 2

ER -

Closed convex sets of Minkowski type

Abstract

Keywords

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