S-Convexity and Gross Substitutability

Author:

Chen Xin1,Li Menglong2ORCID

Affiliation:

1. H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332;

2. Department of Management Sciences, City University of Hong Kong, Hong Kong

Abstract

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.

Publisher

Institute for Operations Research and the Management Sciences (INFORMS)

Subject

Management Science and Operations Research,Computer Science Applications

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