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

  • Authors:

  • Kazuo Murota;Akiyoshi Shioura

  • Affiliations:

  • University of Tokyo, Graduate School of Information Science and Technology, 113-8656, Tokyo, Japan and PRESTO, JST, Tokyo, Japan;Tohoku University, Graduate School of Information Sciences, 980-8579, Sendai, Japan

  • Venue:
  • Mathematical Programming: Series A and B
  • Year:
  • 2004

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Abstract

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.