Motzkin predecomposable sets

A. N. Iusem; J. E. Martínez-Legaz; M. I. Todorov

doi:https://doi.org/10.1007/s10898-013-0097-3

Motzkin predecomposable sets

A. N. Iusem, J. E. Martínez-Legaz, M. I. Todorov

Department of Economics and Economic History

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

11 Citations (Scopus)

Abstract

© 2013, Springer Science+Business Media New York. We introduce and study the family of sets in a finite dimensional Euclidean space which can be written as the Minkowski sum of a compact and convex set and a convex cone (not necessarily closed). We establish several properties of the class of such sets, called Motzkin predecomposable, some of which hold also for the class of Motzkin decomposable sets (i.e., those for which the convex cone in the decomposition is requested to be closed), while others are specific of the new family.

Original language	English
Pages (from-to)	635-647
Journal	Journal of Global Optimization
Volume	60
Issue number	4
DOIs	https://doi.org/10.1007/s10898-013-0097-3
Publication status	Published - 1 Jan 2014

Keywords

Convex cones
Convex sets
Motzkin decomposable sets

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https://ddd.uab.cat/record/182699

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AU - Iusem, A. N.

AU - Martínez-Legaz, J. E.

AU - Todorov, M. I.

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N2 - © 2013, Springer Science+Business Media New York. We introduce and study the family of sets in a finite dimensional Euclidean space which can be written as the Minkowski sum of a compact and convex set and a convex cone (not necessarily closed). We establish several properties of the class of such sets, called Motzkin predecomposable, some of which hold also for the class of Motzkin decomposable sets (i.e., those for which the convex cone in the decomposition is requested to be closed), while others are specific of the new family.

AB - © 2013, Springer Science+Business Media New York. We introduce and study the family of sets in a finite dimensional Euclidean space which can be written as the Minkowski sum of a compact and convex set and a convex cone (not necessarily closed). We establish several properties of the class of such sets, called Motzkin predecomposable, some of which hold also for the class of Motzkin decomposable sets (i.e., those for which the convex cone in the decomposition is requested to be closed), while others are specific of the new family.

KW - Convex cones

KW - Convex sets

KW - Motzkin decomposable sets

U2 - https://doi.org/10.1007/s10898-013-0097-3

DO - https://doi.org/10.1007/s10898-013-0097-3

M3 - Article

SN - 0925-5001

VL - 60

SP - 635

EP - 647

JO - Journal of Global Optimization

JF - Journal of Global Optimization

IS - 4

ER -

Motzkin predecomposable sets

Abstract

Keywords

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