The Pontryagin maximum principle from dynamic programming and viscosity solutions to first-order partial differential equations

Authors:
Emmanuel Nicholas Barron and Robert Jensen

Journal:
Trans. Amer. Math. Soc. **298** (1986), 635-641

MSC:
Primary 49C20; Secondary 35F20, 49B10

DOI:
https://doi.org/10.1090/S0002-9947-1986-0860384-4

MathSciNet review:
860384

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Abstract | References | Similar Articles | Additional Information

Abstract: We prove the Pontryagin Maximum Principle for the Lagrange problem of optimal control using the fact that the value function of the problem is the viscosity solution of the associated Hamilton-Jacobi-Bellman equation. The proof here makes rigorous the formal proof of Pontryagin's principle known for at least three decades.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1986-0860384-4

Keywords:
Pontryagin Maximum Principle,
optimal control,
viscosity solutions,
first-order partial differential equations,
dynamic programming

Article copyright:
© Copyright 1986
American Mathematical Society