Mathematics – Metric Geometry
Scientific paper
2007-06-22
Journal of Mathematical Sciences (Springer, New-York), Vol. 155, No. 6, pp.815--829. Translated from Fundamentalnaya i Priklad
Mathematics
Metric Geometry
20 pages, 1 figure
Scientific paper
10.1007/s10958-008-9243-8
Semimodules over idempotent semirings like the max-plus or tropical semiring have much in common with convex cones. This analogy is particularly apparent in the case of subsemimodules of the n-fold cartesian product of the max-plus semiring it is known that one can separate a vector from a closed subsemimodule that does not contain it. We establish here a more general separation theorem, which applies to any finite collection of closed semimodules with a trivial intersection. In order to prove this theorem, we investigate the spectral properties of certain nonlinear operators called here idempotent cyclic projectors. These are idempotent analogues of the cyclic nearest-point projections known in convex analysis. The spectrum of idempotent cyclic projectors is characterized in terms of a suitable extension of Hilbert's projective metric. We deduce as a corollary of our main results the idempotent analogue of Helly's theorem.
Gaubert Stephane
Sergeev Sergei
No associations
LandOfFree
Cyclic projectors and separation theorems in idempotent convex geometry does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Cyclic projectors and separation theorems in idempotent convex geometry, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Cyclic projectors and separation theorems in idempotent convex geometry will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-188001