Necessary conditions in optimal control and in the calculus of variations

Abstract

The goal of this article is to find, for the two most standard paradigms in dynamic optimization, the simplest proofs that can be based on the techniques invented and refined over the last thirty years in connection with the nonsmooth analysis approach. Specifically, we present a proof of Theorem 2.1 below, which asserts all the first-order necessary conditions for the basic problem in the calculus of variations, and a proof of Theorem 3.1, which is the Pontryagin maximum principle in a classical context.