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Separation of convex sets

✍ Scribed by Jurek Czyzowicz; Eduardo Rivera-Campo; Jorge Urrutia


Publisher
Elsevier Science
Year
1994
Tongue
English
Weight
208 KB
Volume
51
Category
Article
ISSN
0166-218X

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πŸ“œ SIMILAR VOLUMES


On Separation of Plane Convex Sets
✍ Eduardo Rivera-Campo; JenΓΆ TΓΆrΓΆcsik πŸ“‚ Article πŸ“… 1993 πŸ› Elsevier Science 🌐 English βš– 77 KB

We show that in any family \(F\) of \(n \geqslant 5\) convex sets in the plane with pairwise disjoint relative interiors, there are two sets \(A\) and \(B\) such that every line that separates them, separates either \(A\) or \(B\) from at least \((n+28) / 30\) sets in \(F\).

On the separation of convex sets in some
✍ Walter Briec; Charles Horvath πŸ“‚ Article πŸ“… 2011 πŸ› Elsevier Science 🌐 English βš– 163 KB

Two linear maps are usually needed to separate disjoint convex subsets of an idempotent semimodule. In the context of Max-Plus convexity separation can be achieved by a single map if one considers linear maps with values in a linearly ordered semimodule, whose construction is given here, which is no