Mathematical Programming

, Volume 101, Issue 3, pp 415–433 | Cite as

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



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.


combinatorial optimization matroid base polyhedron convex function convex analysis 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  1. 1.Graduate School of Information Science and TechnologyUniversity of TokyoTokyoJapan
  2. 2.Graduate School of Information SciencesTohoku UniversitySendaiJapan
  3. 3.PRESTO, JSTTokyoJapan

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