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Generators, extremals and bases of max cones. (English) Zbl 1119.15018

Authors’ summary: Max cones are max-algebraic analogs of convex cones. We develop a theory of generating sets and extremals of max cones in \(\mathbb R_{+}^n\). 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.

MSC:

15B48 Positive matrices and their generalizations; cones of matrices
15A30 Algebraic systems of matrices

Software:

Scilab
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References:

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