Pontryagin principle and envelope theorem

TL;DR

This paper enhances Pontryagin's maximum principle for optimal control problems by establishing differentiability of the value function under minimal assumptions using Gâteaux and Hadamard differentials.

Contribution

It introduces a refined version of the maximum principle and weakens the differentiability assumptions required for the value function in optimal control.

Findings

Improved maximum principle for optimal control.

Established differentiability of the value function with minimal assumptions.

Utilized Gâteaux and Hadamard differentials for analysis.

Abstract

We provide an improvement of the maximum principle of Pontryagin of the Optimal Control problems. We establish differentiability properties of the value function of problems of Optimal Control with assumptions as low as possible. Notably, we lighten the assumptions by using G\^ateaux and Hadamard differentials.