S-Convexity and Gross Substitutability

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.

Research Progress on Solar Flare Forecast Methods Based on Data-driven Models

“…The overall structure of the model is shown in Figure 8. Chen et al (2022) proposed a two-stage flare forecasting system, the first of which consists of an unsupervised clustering algorithm, k-means, which was used to improve the TP rate, and several CNN models, which improved the flare forecasting rate by integrating the forecasting results of the CNN models. In the second stage, three CNN models were selected: Xception, Resnet18, and Resnet34.…”