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The structure of max–min hyperplanes

✍ Scribed by V. Nitica

Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
485 KB
Volume
432
Category
Article
ISSN
0024-3795

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✦ Synopsis

In this article, continuing [12,13], further contributions to the theory of max-min convex geometry are given. The max-min semiring is the set R = R ∪ {±∞} endowed with the operations ⊕ = max, ⊗ = min in R. A max-min hyperplane (briefly, a hyperplane) is the set of all points x = (x 1 , . . . , x n ) ∈ R n satisfying an equation of the form

, where each side contains at least one term, and where a i / = b i for at least one index i. The main result is a description of a hyperplane in terms of simple polyhedral blocks.

As an application, one shows that the separation of max-min closed convex sets by max-min hyperplanes is not possible in general.

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