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Fundamental Properties of M-convex and L-convex Functions in Continuous Variables (2003)  (Make Corrections)  
Kazuo Murota, Akiyoshi Shioura



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Abstract: The concepts of M-convexity and L-convexity, introduced by Murota (1996,1998) for functions on the integer lattice, extract combinatorial structures in well-solved nonlinear combinatorial optimization problems. These concepts are extended to polyhedral convex functions and quadratic functions on the real space by Murota-Shioura (2000, 2001). In this paper, we consider a further extension to general convex functions. The main aim of this paper is to provide rigorous proofs for fundamental ... (Update)

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BibTeX entry:   (Update)

@misc{ murota-fundamental,
  author = "Kazuo Murota and Akiyoshi Shioura",
  title = "Fundamental Properties of M-convex and L-convex Functions in Continuous
    Variables",
  url = "citeseer.ist.psu.edu/murota03fundamental.html" }
Citations (may not include all citations):
59   Lectures on Functional Equations and Their Applications (context) - Aczel - 1966
42   Submodular Functions and Optimization (context) - Fujishige - 1991
38   Network Flows and Monotropic Optimization (context) - Rockafellar - 1984
33   Discrete convex analysis (context) - Murota - 1998
23   Submodular functions and convexity (context) - Lov - 1983
22   Generalized polymatroids and submodular flows (context) - Frank, Tardos - 1988
20   Convex Functions (context) - Roberts, Varberg - 1973
18   Convexity and Steinitz's exchange property (context) - Murota - 1996
14   Matrices and Matroids for Systems Analysis (context) - Murota - 2000
11   Convexity in nonlinear integer programming (context) - Favati, Tardella - 1990
8   Generalized polymatroids (context) - Frank - 1984
6   Society for Industrial and Ap- plied Mathematics (context) - Murota, Analysis - 2003
4   M-convex function on generalized polyma- troid - Murota, Shioura - 1999
3   Discrete Convex Analysis--An Introduction (context) - Murota - 2001
3   Extension of M-convexity and L-convexity to polyhedral conve.. (context) - Murota, Shioura - 2000
2   Discrete convexity and equilibria in economies with indivisi.. - Danilov, Koshevoy et al. - 2001
2   Some easily solvable nonlinear integer programs (context) - Camerini, Conforti et al. - 1989
1   Notes on L-/M-convex functions and the separation theorems (context) - Fujishige, Murota - 2000
1   On minimizing nonseparable functions defined on the in- tege.. (context) - Miller - 1971
1   New characterizations of M-convex functions and their applic.. (context) - Murota, Tamura
1   Transportation and Scheduling--Theory and Al- gorithms (context) - Iri, Flow - 1969
1   Application of M-convex submodular flow problem to mathemati.. (context) - Murota, Tamura
1   convex and L-convex functions (context) - Murota, Shioura et al. - 2001
1   Conjugacy relationship between M-convex and L-convex functio.. (context) - Murota, Shioura

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