Generators, Extremals and Bases of Max Cones

Peter Butkovic*, Hans Schneider, Sergei Sergeev

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

50 Citations (Scopus)


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 . 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.

Original languageEnglish
Pages (from-to)394-406
Number of pages13
JournalLinear Algebra and its Applications
Issue number2-3
Publication statusPublished - 1 Mar 2007


  • basis
  • max algebra
  • extremal
  • cone
  • scaling
  • algorithm


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