Nonstandard Tools for Nonsmooth Analysis

TL;DR

This paper reviews nonsmooth analysis tools based on nonstandard set theory models, illustrating their application with a criterion for infinitesimal optimality in discrete dynamic systems.

Contribution

It introduces a nonstandard set theory approach to nonsmooth analysis and demonstrates its use in deriving optimality criteria for discrete systems.

Findings

Provides a criterion for infinitesimal optimal paths in discrete systems

Connects nonstandard models with nonsmooth analysis tools

Offers a theoretical framework for nonsmooth optimization

Abstract

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.