M-convex and L-convex Fuctions over the Real Space
نویسندگان
چکیده
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 this paper is to provide rigorous proofs for the fundamental results of general M-convex and L-convex functions over the real space. In particular, we prove that the conjugacy relationship holds for general M-convex and L-convex functions over the real space.
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