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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

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
MathSciNet review: 860384
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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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DOI: http://dx.doi.org/10.1090/S0002-9947-1986-0860384-4
PII: S 0002-9947(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