
Journal of Convex Analysis 19 (2012), No. 2, 485496 Copyright Heldermann Verlag 2012 Lexicographical Representation of Convex Sets Juan Enrique MartínezLegaz Departament d'Economia i d'Història Econòmica, Universitat Autònoma de Barcelona, 08193 Bellaterra, Spain JuanEnrique.Martinez.Legaz@uab.cat José VicentePérez Departamento de Estadística e Investigación Operativa, Universidad de Alicante, 03080 Alicante, Spain Jose.Vicente@ua.es We introduce two new families of properties on convex sets of R^{n}, in order to establish new theorems regarding open and closed separation of a convex set from any outside point by linear operators from R^{n} to R^{m}, in the sense of the lexicographical order of R^{m}, for each m = 1, 2, ... , n. We thus obtain lexicographical extensions of well known separation theorems for convex sets as well as characterizations of the solution sets of lexicographical (weak and strict) inequality systems defined by matrices of a given rank. Keywords: Convex sets, open lexicographical separation, closed lexicographical separation. MSC: 52A20, 90C25 [ Fulltextpdf (133 KB)] for subscribers only. 