Motzkin predecomposable sets
type: Item
instance of: scholarly article
title: Motzkin predecomposable sets
zbMATH Open document ID: 1305.52004
published in: Journal of Global Optimization
publication date: 2014-11-27T00:00:00Z
full work available at URL: http://ddd.uab.cat/record/182699
review text: The authors introduce and study a family of sets in a finite dimensional Euclidean space. Definition: A nonempty set \(F\subset\mathbb R^n\) is Motzkin predecomposable (M-predecomposable) if there exists a compact convex set \(C\) and a convex cone \(D\) such that \(F = C + D\). They show that the class of M-predecomposable sets is invariant under affine maps and Minkowski sums. They also show that faces of M-predecomposable sets are M-predecomposable as well as the existence of minimal decomposition of M-predecomposable sets. They also provide two characterizations of M-predecomposable sets both related to some properties of their faces.
Mathematics Subject Classification ID: 52A07
Mathematics Subject Classification ID: 54F65
zbMATH DE Number: 6374615
zbMATH Keywords: Motzkin decomposable sets
zbMATH Keywords: convex sets
zbMATH Keywords: convex cones
author: Alfredo Iusem
author: Juan-Enrique Martínez-Legaz
author: Maxim Ivanov Todorov
reviewed by: Şafak Alpay
MaRDI profile type: Publication
OpenAlex ID: W1969299363
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DOI: 10.1007/S10898-013-0097-3
description: scientific article; zbMATH DE number 6374615