English

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