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M-convex and L-convex Fuctions over the Real Space Two Conjugate Classes of Combinatorial Convex Functions (2002)  (Make Corrections)  
Kazuo Murota, Akiyoshi Shioura



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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 defined over the real space. In this paper, we consider a further extension to more general convex functions defined over the real space. The main aim of... (Update)

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BibTeX entry:   (Update)

@misc{ murota-mconvex,
  author = "Kazuo Murota and Akiyoshi Shioura",
  title = "M-convex and L-convex Fuctions over the Real Space - Two Conjugate Classes
    of Combinatorial Convex Functions",
  url = "citeseer.ist.psu.edu/murota02mconvex.html" }
Citations (may not include all citations):
201   Nonlinear Programming: Theory and Algorithms (context) - Bazaraa, Sherali et al. - 1993
59   Lectures on Functional Equations and Their Applications (context) - Aczel - 1966
2   Some easily solvable nonlinear integer programs (context) - Camerini, Conforti et al. - 1989

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