Directed Discrete Midpoint Convexity

On Basic Operations Related to Network Induction of Discrete Convex Functions

“…With this correspondence, Theorem 2.2 of [30] for valuated delta-matroids is translated into this theorem. Such characterization fails for (global and local) discrete midpoint convexity, as pointed out recently by [53]. That is, there is a function f which is not discrete midpoint convex but for which arg min f [−c] is discrete midpoint convex for every c.…”