Quadratic M-convex and L-convex functions

Kazuo Murota, Akiyoshi Shioura

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)


The concepts of L-convexity and M-convexity are introduced by Murota (1996) for functions defined over the integer lattice, and recently extended to polyhedral convex functions by Murota-Shioura (2000). L-convex and M-convex functions are deeply connected with well-solvability in combinatorial optimization problems with convex objective functions. In this paper, we consider these concepts for quadratic functions and the structure of the coefficient matrices of such quadratic functions. It is shown that quadratic L-convex and M-convex functions can be characterized by nice combinatorial properties of their coefficient matrices. The conjugacy relationship between quadratic L-convex and M-convex functions is also discussed.

Original languageEnglish
Pages (from-to)318-341
Number of pages24
JournalAdvances in Applied Mathematics
Issue number2
Publication statusPublished - 2004 Aug
Externally publishedYes


  • Base polyhedron
  • Discrete optimization
  • Matroid
  • Quadratic function

ASJC Scopus subject areas

  • Applied Mathematics


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