On the characterization of some families of closed convex sets

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Title: On the characterization of some families of closed convex sets
Authors: Goberna, Miguel A. | Jornet Pla, Valentín | Rodríguez Álvarez, Margarita
Research Group/s: Programación Semi-infinita
Center, Department or Service: Universidad de Alicante. Departamento de Estadística e Investigación Operativa
Keywords: Closed convex sets | Simplices | Sandwiches | Parallelotopes | Linear inequalities | Connectivity
Knowledge Area: Matemáticas
Issue Date: 2002
Publisher: Heldermann Verlag
Citation: 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
Abstract: 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.
Sponsor: This work was supported by the DGES of Spain, Grant PB98-0975.
URI: http://hdl.handle.net/10045/8804
ISSN: 0138-4821
Language: eng
Type: info:eu-repo/semantics/article
Peer Review: si
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