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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Optimal control and semicontinuous viscosity solutions


Authors: E. N. Barron and R. Jensen
Journal: Proc. Amer. Math. Soc. 113 (1991), 397-402
MSC: Primary 49L25; Secondary 49J45
MathSciNet review: 1076572
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Abstract: We study the value function for an optimal control problem with upper semicontinuous terminal data. We prove that the upper semicontinuous envelope of the value function is the unique semicontinuous viscosity solution of the Bellman equation and that it coincides with the value function obtained when using relaxed controls.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1991-1076572-8
PII: S 0002-9939(1991)1076572-8
Keywords: Optimal control, semicontinuous data, semicontinuous viscosity solutions, relaxed controls
Article copyright: © Copyright 1991 American Mathematical Society