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

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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.

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Authors and Affiliations

  1. Graduate School of Information Science and Technology, University of Tokyo, Tokyo, 113-8656, Japan

    Kazuo Murota

  2. Graduate School of Information Sciences, Tohoku University, Sendai, 980-8579, Japan

    Akiyoshi Shioura

  3. PRESTO, JST, Tokyo, Japan

    Kazuo Murota

Authors
  1. Kazuo Murota
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  2. Akiyoshi Shioura
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Corresponding author

Correspondence to Akiyoshi Shioura.

Additional information

Mathematics Subject Classification (1991): 90C10, 90C25, 90C27, 90C35

This work is supported by Grant-in-Aid of the Ministry of Education, Culture, Sports, Science and Technology of Japan

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Murota, K., Shioura, A. Conjugacy relationship between M-convex and L-convex functions in continuous variables. Math. Program., Ser. A 101, 415–433 (2004). https://doi.org/10.1007/s10107-003-0478-3

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  • DOI: https://doi.org/10.1007/s10107-003-0478-3

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