Weakly Motzkin Predecomposable Sets

J. E. Martínez-Legaz; M. I. Todorov

doi:https://doi.org/10.1007/s11228-017-0420-0

Weakly Motzkin Predecomposable Sets

J. E. Martínez-Legaz, M. I. Todorov

Department of Economics and Economic History

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

3 Citations (Scopus)

Abstract

© 2017, Springer Science+Business Media Dordrecht. We introduce and study the class of weakly Motzkin predecomposable sets, which are those sets in ℝ n that can be expressed as the Minkowski sum of a bounded convex set and a convex cone, none of them being necessarily closed. This class contains that of Motzkin predecomposable sets, for which the bounded components are compact, which in turn contains the class of Motzkin decomposable sets, for which the bounded components are compact and the conic components are closed.

Original language	English
Pages (from-to)	507-516
Journal	Set-Valued and Variational Analysis
Volume	25
Issue number	3
DOIs	https://doi.org/10.1007/s11228-017-0420-0
Publication status	Published - 1 Sept 2017

Keywords

Convex cones
Convex sets
Motzkin decomposable sets

Access to Document

https://doi.org/10.1007/s11228-017-0420-0

https://ddd.uab.cat/record/197034

Cite this

@article{600200164f1243d48f7ed3bc3c437c74,

title = "Weakly Motzkin Predecomposable Sets",

abstract = "{\textcopyright} 2017, Springer Science+Business Media Dordrecht. We introduce and study the class of weakly Motzkin predecomposable sets, which are those sets in ℝ n that can be expressed as the Minkowski sum of a bounded convex set and a convex cone, none of them being necessarily closed. This class contains that of Motzkin predecomposable sets, for which the bounded components are compact, which in turn contains the class of Motzkin decomposable sets, for which the bounded components are compact and the conic components are closed.",

keywords = "Convex cones, Convex sets, Motzkin decomposable sets",

author = "Mart{\'i}nez-Legaz, {J. E.} and Todorov, {M. I.}",

year = "2017",

month = sep,

day = "1",

doi = "https://doi.org/10.1007/s11228-017-0420-0",

language = "English",

volume = "25",

pages = "507--516",

number = "3",

}

TY - JOUR

T1 - Weakly Motzkin Predecomposable Sets

AU - Martínez-Legaz, J. E.

AU - Todorov, M. I.

PY - 2017/9/1

Y1 - 2017/9/1

N2 - © 2017, Springer Science+Business Media Dordrecht. We introduce and study the class of weakly Motzkin predecomposable sets, which are those sets in ℝ n that can be expressed as the Minkowski sum of a bounded convex set and a convex cone, none of them being necessarily closed. This class contains that of Motzkin predecomposable sets, for which the bounded components are compact, which in turn contains the class of Motzkin decomposable sets, for which the bounded components are compact and the conic components are closed.

AB - © 2017, Springer Science+Business Media Dordrecht. We introduce and study the class of weakly Motzkin predecomposable sets, which are those sets in ℝ n that can be expressed as the Minkowski sum of a bounded convex set and a convex cone, none of them being necessarily closed. This class contains that of Motzkin predecomposable sets, for which the bounded components are compact, which in turn contains the class of Motzkin decomposable sets, for which the bounded components are compact and the conic components are closed.

KW - Convex cones

KW - Convex sets

KW - Motzkin decomposable sets

U2 - https://doi.org/10.1007/s11228-017-0420-0

DO - https://doi.org/10.1007/s11228-017-0420-0

M3 - Article

SN - 1877-0533

VL - 25

SP - 507

EP - 516

JO - Set-Valued and Variational Analysis

JF - Set-Valued and Variational Analysis

IS - 3

ER -

Weakly Motzkin Predecomposable Sets

Abstract

Keywords

Access to Document

Fingerprint

Cite this