About: K-convex function

K-convex functions, first introduced by Scarf, are a special weakening of the concept of convex function which is crucial in the proof of the optimality of the policy in inventory control theory. The policy is characterized by two numbers s and S, , such that when the inventory level falls below level s, an order is issued for a quantity that brings the inventory up to level S, and nothing is ordered otherwise. Gallego and Sethi have generalized the concept of K-convexity to higher dimensional Euclidean spaces.