On Motzkin decomposable sets and functions

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:372

Article

Goberna, M. A.¹  Martinez-Legaz, J. E.²  Todorov, M. I.³ 

[1] Univ Alicante, Dept Stat & Operat Res, Alicante, Spain

[2] Univ Autonoma Barcelona, Dept Econ & Econ Hist, Barcelona, Spain

[3] Univ Americas Puebla, Dept Actuary & Math, Cholula, Mexico

关键词: Motzkin decomposition;    Closed convex sets;    Convex functions;   

DOI  :  10.1016/j.jmaa.2010.07.007

来源: Elsevier

【 摘 要 】

A set is called Motzkin decomposable when it can be expressed as the Minkowski sum of a compact convex set with a closed convex cone. The main result in this paper establishes that a closed convex set is Motzkin decomposable if and only if the set of extreme points of its intersection with the linear subspace orthogonal to its lineality is bounded. The paper characterizes the class of the extended functions whose epigraphs are Motzkin decomposable sets showing, in particular, that these functions attain their global minima when they are bounded from below. Calculus of Motzkin decomposable sets and functions is provided. (C) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

Free