Best approximation in max-plus semimodules

Details Best approximation in max-plus semimodules Best approximation in max-plus semimodules

2010-12-26

arxiv.org/abs/1012.5492v1

Linear Algebra and its Applications Volume 435, Issue 12, 15 December 2011, Pages 3261-3296

Mathematics

Metric Geometry

42 pages and 4 figures

Scientific paper

10.1016/j.laa.2011.06.009

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.

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