The tropical analogue of polar cones

Understand

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.