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arXiv · 0805.3688

The tropical analogue of polar cones

Stéphane Gaubert·Ricardo D. Katz
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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.

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Stéphane Gaubert, Ricardo D. Katz. 2009-07-23. The tropical analogue of polar cones. https://doi.org/10.1016/j.laa.2009.03.012

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