Motzkin decomposition of closed convex sets
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Title: | Motzkin decomposition of closed convex sets |
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Authors: | Goberna, Miguel A. | González, E. | Martínez Legaz, Juan Enrique | Todorov, Maxim I. |
Research Group/s: | Programación Semi-infinita |
Center, Department or Service: | Universidad de Alicante. Departamento de Estadística e Investigación Operativa | Universitat Autònoma de Barcelona. Departament d'Economia i d'Història Econòmica | Universidad de las Américas Puebla. Departamento de Física y Matemáticas |
Keywords: | Closed convex sets | Linear inequality systems | Semi-infinite optimization |
Knowledge Area: | Estadística e Investigación Operativa |
Issue Date: | 8-Oct-2009 |
Publisher: | Elsevier |
Citation: | GOBERNA TORRENT, Miguel Ángel, et al. “Motzkin decomposition of closed convex sets”. Journal of Mathematical Analysis and Applications. Vol. 364, No. 1 (1 Apr. 2010). ISSN 0022-247X, pp. 209-221 |
Abstract: | Theodore Motzkin proved, in 1936, that any polyhedral convex set can be expressed as the (Minkowski) sum of a polytope and a polyhedral convex cone. This paper provides five characterizations of the larger class of closed convex sets in finite dimensional Euclidean spaces which are the sum of a compact convex set with a closed convex cone. These characterizations involve different types of representations of closed convex sets as the support functions, dual cones and linear systems whose relationships are also analyzed in the paper. The obtaining of information about a given closed convex set F and the parametric linear optimization problem with feasible set F from each of its different representations, including the Motzkin decomposition, is also discussed. |
Sponsor: | This work has been supported by MICINN of Spain, Grants MTM2008-06695-C03-01/03, by Generalitat Valenciana, by Generalitat de Catalunya, by the Barcelona GSE Research Network, and by CONACyT of Mexico, Grant 55681. |
URI: | http://hdl.handle.net/10045/15414 |
ISSN: | 0022-247X (Print) | 1096-0813 (Online) |
DOI: | 10.1016/j.jmaa.2009.10.015 |
Language: | eng |
Type: | info:eu-repo/semantics/article |
Peer Review: | si |
Publisher version: | http://dx.doi.org/10.1016/j.jmaa.2009.10.015 |
Appears in Collections: | INV - LOPT - Artículos de Revistas |
Files in This Item:
File | Description | Size | Format | |
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Goberna_Motzkin_decomposition_Preprint.pdf | Preprint (acceso libre) | 223,57 kB | Adobe PDF | Open Preview |
Goberna_Motzkin_decomposition_Final.pdf | Versión final (acceso restringido) | 275,96 kB | Adobe PDF | Open Request a copy |
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