K-convex function

K-convex functions, first introduced by Scarf,^[1] are a special weakening of the concept of convex function which is crucial in the proof of the optimality of the $(s,S)$ policy in inventory control theory. The policy is characterized by two numbers $s$ and $S$ , $S\geq s$ , 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 ^[2] have generalized the concept of K-convexity to higher dimensional Euclidean spaces.

^ Scarf, H. (1960). The Optimality of (S, s) Policies in the Dynamic Inventory Problem. Stanford, CA: Stanford University Press. p. Chapter 13.
^ Gallego, G. and Sethi, S. P. (2005). K-convexity in ℜⁿ. Journal of Optimization Theory & Applications, 127(1):71-88.

[Scarf-1] Scarf, H. (1960). The Optimality of (S, s) Policies in the Dynamic Inventory Problem. Stanford, CA: Stanford University Press. p. Chapter 13.

[sethigallego-2] Gallego, G. and Sethi, S. P. (2005). K-convexity in ℜⁿ. Journal of Optimization Theory & Applications, 127(1):71-88.

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