Lexicographical representation of convex sets

Juan Enrique Martínez-Legaz, José Vicente-Pérez

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3 Citations (Scopus)


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,..., 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. © Heldermann Verlag.
Original languageEnglish
Pages (from-to)485-496
JournalJournal of Convex Analysis
Issue number2
Publication statusPublished - 30 Aug 2012


  • Closed lexicographical separation
  • Convex sets
  • Open lexicographical separation


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