Generators, extremals and bases of max cones
By Peter Butkovic, Hans Schneider, Sergeĭ Sergeev. 2006
115 citations recorded by the source corpus.
Abstract Max cones are max-algebraic analogs of convex cones. In the present paper we develop a theory of generating sets and extremals of max cones in R + n . This theory is based on the observation that extremals are minimal elements of max cones under suitable scalings of vectors. We give new proofs of existing results suitably generalizing, restating and refining them. Of these, it is important that any set of generators may be partitioned into the set of extremals and the set of redundant elements. We include results on properties of open and closed cones, on properties of totally dependent sets and on computational bounds for the problem of finding the (essentially unique) basis of a finitely generated cone.
Subfields: Applied Mathematics, Computational Theory and Mathematics
View Paper: https://www.semanticscholar.org/paper/222de3ddfb448b6f8e32ea5c46dad40bde2905a9
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In Applied Mathematics
In Computational Theory and Mathematics
Citations in the corpus
- Minimal half-spaces and external representation of tropical polyhedra (2009, background): “Some of the previously mentioned researchers, and some other ones, including Allamigeon, Butkovič, Goubault, Katz, Nitica, Meunier, Sergeev, Schneider, have recently made a number of works in the field, we refer the reader to [AGK09, BSS07, GK06, GK07, NS07, JSY07, Jos08, GK09, GM09, AGG09] for a r”