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

Barron, Emmanuel Nicholas; Jensen, Robert

doi:10.1090/S0002-9947-1986-0860384-4

The Pontryagin maximum principle from dynamic programming and viscosity solutions to first-order partial differential equations
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by Emmanuel Nicholas Barron and Robert Jensen PDF

Trans. Amer. Math. Soc. 298 (1986), 635-641 Request permission

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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The mathematical theory of optimal processes