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Reports (Research Report) Year : 2002

Duality and Separation Theorems in Idempotent Semimodules


We consider subsemimodules and convex subsets of semimodules over semirings with an idempotent addition. We introduce nonlinear projection on subsemimod- ules: the projection of a point is the maximal approximation from below of the point in the subsemimodule. We use this projection to separate a point from a convex set. We also show that the projection minimizes the analogue of Hilbert's projective metric. We develop more generally a theory of dual pairs for idempotent semimodules. We obtain as a corollary duality results between the row and column spaces of matrices with entries in idempotent semirings. We illustrate the results by showing polyhedra and half-spaces over the max-plus semiring.
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Dates and versions

inria-00071917 , version 1 (23-05-2006)


  • HAL Id : inria-00071917 , version 1


Guy Cohen, Stéphane Gaubert, Jean-Pierre Quadrat. Duality and Separation Theorems in Idempotent Semimodules. [Research Report] RR-4668, INRIA. 2002. ⟨inria-00071917⟩
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