| Título: | Motzkin decomposition of closed convex sets |
| Autores: |
Goberna Torrent, Miguel Ángel González, E. Martínez Legaz, Juan Enrique Todorov, Maxim I. |
| Fecha: |
2010-11-19 2010-11-19 2009-10-08 |
| Publicador: | RUA Docencia |
| Fuente: |
 |
| Tipo: | info:eu-repo/semantics/article |
| Tema: |
Closed convex sets Linear inequality systems Semi-infinite optimization Estadística e Investigación Operativa |
| Descripción: |
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. 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. |
| Idioma: | Inglés |
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