An approach to discrete convexity and its use in an optimal fleet mix problem

Abstract

A notion of convexity for discrete functions is first introduced, with the aim to guarantee both the increasing monotonicity of marginal increments and the convexity of the sum of convex functions. Global optimality of local minima is then studied both for single variable functions and for multi variables ones. Finally, a concrete optimal fleet mix problem is studied, pointing out its discrete convexity properties.