On the characterization of some families of closed convex sets
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Título: | On the characterization of some families of closed convex sets |
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Autor/es: | Goberna, Miguel A. | Jornet Pla, Valentín | Rodríguez Álvarez, Margarita |
Grupo/s de investigación o GITE: | Programación Semi-infinita |
Centro, Departamento o Servicio: | Universidad de Alicante. Departamento de Estadística e Investigación Operativa |
Palabras clave: | Closed convex sets | Simplices | Sandwiches | Parallelotopes | Linear inequalities | Connectivity |
Área/s de conocimiento: | Matemáticas |
Fecha de publicación: | 2002 |
Editor: | Heldermann Verlag |
Cita bibliográfica: | GOBERNA TORRENT, Miguel Ángel; JORNET PLA, Valentín; RODRÍGUEZ ÁLVAREZ, Margarita. “On the characterization of some families of closed convex sets”. Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry. Vol. 43, No. 1 (2002). ISSN 0138-4821, pp. 153-169 |
Resumen: | This paper deals with the characterization of the sums of compact convex sets with linear subspaces, simplices, sandwiches (convex hulls of pairs of parallel affine manifolds) and parallelotopes in terms of the so-called internal and conical representations, topological and geometrical properties. In particular, it is shown that a closed convex set is a sandwich if and only if its relative boundary is unconnected. The characterizations of families of closed convex sets can be useful in different fields of applied mathematics. For instance, it is proved that a bounded linear semi-infinite programming problem whose feasible set is the sum of a compact convex set with a linear subspace is necessarily solvable and has zero duality gap. |
Patrocinador/es: | This work was supported by the DGES of Spain, Grant PB98-0975. |
URI: | http://hdl.handle.net/10045/8804 |
ISSN: | 0138-4821 |
Idioma: | eng |
Tipo: | info:eu-repo/semantics/article |
Revisión científica: | si |
Aparece en las colecciones: | INV - LOPT - Artículos de Revistas |
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GJR02.pdf | Versión revisada (acceso libre) | 156,05 kB | Adobe PDF | Abrir Vista previa |
b43h1gob.pdf | Versión final (acceso libre) | 198,76 kB | Adobe PDF | Abrir Vista previa |
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