S-Convexity and Gross Substitutability
Chen和Li提出了连续空间上的S-凸函数概念，扩展了离散凸分析中的M-自然凸函数，并证明了S-凹性是刻画可分商品市场中总替代性的正确概念。
A New Concept to Study Substitute Structures in Economics and Operations Models In “S-Convexity and Gross Substitutability,” Chen and Li propose a novel concept of S-convex functions defined on continuous spaces, which extends a key concept of M-natural-convex functions in discrete convex analysis. They develop a host of fundamental properties and characterizations of S-convex functions. In a parametric maximization model with a box constraint, they show that the set of optimal solutions is nonincreasing in the parameters if the objective function is S-concave and prove the necessity of S-concavity under some conditions. The monotonicity result finds notable inventory models. Interestingly, the authors show that S-concavity is the correct notion characterizing gross substitutability, an important concept in economics for markets with divisible goods.