Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:	Prof. Xin Chen，Department of Industrial and Enterprise Systems Engineering, University of Illinois at Urbana
Inviter:	刘歆副研究员和刘亚锋副研究员
Title:	M-Natural-Convexity and Its Applications in Operations
Time & Venue:	2020.01.08 15:00-16:00 Z311
Abstract:	M-natural-convexity, one of the main concepts in discrete convex analysis, possesses many salient structural properties and allows for the design of efficient algorithms. In this talk, we discuss several new fundamental properties of M-natural-convexity and introduce its extension: S(ubsitute)-convexity. In particular, we show that in a parametric minimization model, the optimal solution is nonincreasing in the parameters when the objective function is S-convex and the constraint is a box. We then utilize our results to analyze two important operations models: a classical multi-product dynamic stochastic inventory model, and a portfolio contract model where a buyer reserves capacities in blocks from multiple competing suppliers. We illustrate that looking from the lens of M-natural-convexity allows to simplify the complicated analysis in the literature for each model and extend the results to more general settings.