Fundamental Properties of M-Convex and L-Convex Functions in Continuous Variables

Kazuo MUROTA  Akiyoshi SHIOURA  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E87-A   No.5   pp.1042-1052
Publication Date: 2004/05/01
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Discrete Mathematics and Its Applications)
combinatorial optimization,  matroid,  base polyhedron,  convex function,  convex analysis,  

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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 properties of general M-convex and L-convex functions.