Max-plus convex geometry

Authors:
Stéphane Gaubert;Ricardo Katz
Affiliations:
Domaine de Voluceau, INRIA, Le Chesnay, France;CONICET, Instituto de Matemática “Beppo Levi”, Universidad Nacional de Rosario, Rosario, Argentina
Venue:
RelMiCS'06/AKA'06 Proceedings of the 9th international conference on Relational Methods in Computer Science, and 4th international conference on Applications of Kleene Algebra
Year:
2006

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Abstract

Max-plus analogues of linear spaces, convex sets, and polyhedra have appeared in several works. We survey their main geometrical properties, including max-plus versions of the separation theorem, existence of linear and non-linear projectors, max-plus analogues of the Minkowski-Weyl theorem, and the characterization of the analogues of “simplicial” cones in terms of distributive lattices.