M-natural/S-Convexity and Applications

Department of Decision Sciences and Managerial Economics


Classical monotone comparative statics in parametric optimization problems establishes the existence of nondecreasing optimal solutions (in parameters) through lattice programming. In this talk, we use M-natural-convexity, one of the key concepts in discrete convex analysis, and introduce a new concept of S-convexity as its extension to develop monotone comparative statics in parallel to lattice programming. Specifically, we show that in a parametric minimization model, the optimal solution (set) is nonincreasing (instead of nondecreasing) in the parameters when the objective function is M-natural/S-convex and the constraint is a box, and M-natural/S-convexity is preserved under the optimization operation. We illustrate their applications on several operations models including a multi-product newsvendor model with a joint capacity and a portfolio contract model.