Goberna, Miguel A., Jornet Pla, Valentín, Rodríguez Álvarez, Margarita
On the characterization of some families of closed convex sets
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
URI: http://hdl.handle.net/10045/8804
DOI: 
ISSN: 0138-4821
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.
Keywords:Closed convex sets, Simplices, Sandwiches, Parallelotopes, Linear inequalities, Connectivity
Heldermann Verlag
info:eu-repo/semantics/article