The tropical analogue of polar cones
Metric Geometry
2009-07-23 v2 Optimization and Control
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.
Keywords
Cite
@article{arxiv.0805.3688,
title = {The tropical analogue of polar cones},
author = {Stéphane Gaubert and Ricardo D. Katz},
journal= {arXiv preprint arXiv:0805.3688},
year = {2009}
}
Comments
21 pages, 3 figures, example added, figures improved, notation changed