This is an overview of the basic tools of nonsmooth analysis which are grounded on nonstandard models of set theory. By way of illustration we give a criterion for an infinitesimally optimal path of a general discrete dynamic system.
Calculus reduces forecast to numbers, which is scalarization in modern parlance. Spontaneous solutions are often labile and rarely optimal. Thus, nonsmooth analysis deals with inequality, scalarization and stability. Some aspects of the latter are revealed by the tools of nonstandard models to be discussed.