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K-convex function
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<p><i>K</i>-convex functions, first introduced by <a href="/facts/Herbert_Scarf/cBGgw8jp">Scarf</a>, are a special weakening of the concept of <a href="/facts/Convex_function/IbzG5SLF">convex function</a> which is crucial in the proof of the <a href="/facts/Mathematical_optimization/oRn8Iv5I">optimality</a> of the ( s , S ) {\displaystyle (s,S)} policy in <a href="/facts/Inventory_theory/Yy9QMRKT">inventory control theory</a>. The policy is characterized by two numbers s and S, S ≥ s {\displaystyle 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 have generalized the concept of <i>K</i>-convexity to higher dimensional Euclidean spaces. </p>