Fundamental properties of M-convex and L-convex functions in continuous variables

Kazuo Murota, Akiyoshi Shioura

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)


The concepts of M-convexity and L-convexity, introduced by Murota (1996, 1998) for functions on the integer lattice, extract combinatorial structures in well-solved nonlinear combinatorial optimization problems. These concepts are extended to polyhedral convex functions and quadratic functions on the real space by Murota-Shioura (2000, 2001). In this paper, we consider a further extension to general convex functions. The main aim of this paper is to provide rigorous proofs for fundamental properties of general M-convex and L-convex functions.

Original languageEnglish
Pages (from-to)1042-1052
Number of pages11
JournalIEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Issue number5
Publication statusPublished - 2004 May


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

ASJC Scopus subject areas

  • Signal Processing
  • Computer Graphics and Computer-Aided Design
  • Electrical and Electronic Engineering
  • Applied Mathematics


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