On linear systems containing strict inequalities

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Title: On linear systems containing strict inequalities
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: Linear systems | Strict linear inequalities | Evenly convex sets | Semi-infinite programming
Knowledge Area: Matemáticas
Issue Date: 1-Feb-2003
Publisher: Elsevier
Citation: GOBERNA TORRENT, Miguel Ángel; JORNET PLA, Valentín; RODRÍGUEZ ÁLVAREZ, Margarita. “On linear systems containing strict inequalities”. Linear Algebra and its Applications. Vol. 360 (1 Febr. 2003). ISSN 0024-3795, pp. 151-171
Abstract: This paper deals with systems of an arbitrary (possibly infinite) number of both weak and strict linear inequalities. We analize the existence of solutions for such kind of systems and show that the large class of convex sets which admit this kind of linear representations (i.e., the so-called evenly convex sets) enjoys most of the well-known properties of the subclass of the closed convex sets. We also show that it is possible to obtain geometrical information on these sets from a given linear representation. Finally, we discuss the theory and methods for those linear optimization problems which contain strict inequalities as constraints.
Sponsor: DGES of Spain, Grant PB98-0975.
URI: http://hdl.handle.net/10045/8163
ISSN: 0024-3795
DOI: 10.1016/S0024-3795(02)00445-7
Language: eng
Type: info:eu-repo/semantics/article
Peer Review: si
Publisher version: http://dx.doi.org/10.1016/S0024-3795(02)00445-7
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