Hahn-Banach Separation Theorem for Max-Plus Semimodules
نویسندگان
چکیده
We introduce max-plus analogues of basic Euclidian geometry notions: scalar product is replaced by a scalar division, and the associated distance is essentially Hilbert’s projective distance. We introduce an orthogonal projection and prove a Hahn-Banach type theorem: a point can be separated from a semimodule by a hyperplane orthogonal to the direction of projection. We use these results to separate max-plus convex sets, and illustrate this new geometry by twodimensional examples.
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