Quasi M-convex and L-convex functions—quasiconvexity in discrete optimization Original Research Article

We introduce two classes of discrete quasiconvex functions, called quasi M- and L-convex functions, by generalizing the concepts of M- and L-convexity due to Murota (Adv. Math. 124 (1996) 272) and (Math. Programming 83 (1998) 313). We investigate the structure of quasi M- and L-convex functions with respect to level sets, and show that various greedy algorithms work for the minimization of quasi M- and L-convex functions.