Best approximation in max-plus semimodules
Metric Geometry
2011-11-08 v1 Rings and Algebras
Abstract
We establish new results concerning projectors on max-plus spaces, as well as separating half-spaces, and derive an explicit formula for the distance in Hilbert's projective metric between a point and a half-space over the max-plus semiring, as well as explicit descriptions of the set of minimizers. As a consequence, we obtain a cyclic projection type algorithm to solve systems of max-plus linear inequalities.
Cite
@article{arxiv.1012.5492,
title = {Best approximation in max-plus semimodules},
author = {Marianne Akian and Stephane Gaubert and Viorel Nitica and Ivan Singer},
journal= {arXiv preprint arXiv:1012.5492},
year = {2011}
}
Comments
42 pages and 4 figures