1-2hit |
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.
This note investigates the characterizing properties of the level sets of an M-convex function introduced by Murota.