Conjugacy relationship between M-convex and L-convex functions in continuous variables

Kazuo Murota, Akiyoshi Shioura

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)


By extracting combinatorial structures in well-solved nonlinear combinatorial optimization problems, Murota (1996,1998) introduced the concepts of M-convexity and L-convexity to functions defined over the integer lattice. Recently, Murota-Shioura (2000, 2001) extended these concepts to polyhedral convex functions and quadratic functions in continuous variables. In this paper, we consider a further extension to more general convex functions defined over the real space, and provide a proof for the conjugacy relationship between general M-convex and L-convex functions.

Original languageEnglish
Pages (from-to)415-433
Number of pages19
JournalMathematical Programming
Issue number3
Publication statusPublished - 2004 Dec 1


  • Base polyhedron
  • Combinatorial optimization
  • Convex analysis
  • Convex function
  • Matroid

ASJC Scopus subject areas

  • Software
  • Mathematics(all)


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