The tropical analogue of polar cones

Abstract

We study the max-plus or tropical analogue of the notion of polar: the polar of a cone represents the set of linear inequalities satisfied by its elements. We establish an analogue of the bipolar theorem, which characterizes all the inequalities satisfied by the elements of a tropical convex cone. We derive this characterization from a new separation theorem. We also establish variants of these results concerning systems of linear equalities.

21 pages, 3 figures, example added, figures improved, notation changed

References in corpus (4)

• Duality and separation theorems in idempotent semimodules
• The Minkowski Theorem for Max-plus Convex Sets
• Rational semimodules over the max-plus semiring and geometric approach of discrete event systems
• Carathéodory, Helly and the others in the max-plus world