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Title: Viscosity Solutions for McKean–Vlasov Control on a Torus
An optimal control problem in the space of probability measures, and the viscosity solu- tions of the corresponding dynamic programming equations defined using the intrinsic linear derivative are studied. The value function is shown to be Lipschitz continuous with respect to a novel smooth Fourier-Wasserstein metric. A comparison result between the Lipschitz viscosity sub and super solutions of the dynamic programming equation is proved using this metric, characterizing the value function as the unique Lipschitz viscosity solution.  more » « less
Award ID(s):
2106462
PAR ID:
10519301
Author(s) / Creator(s):
;
Publisher / Repository:
Archiv
Date Published:
Journal Name:
SIAM Journal on Control and Optimization
Volume:
62
Issue:
2
ISSN:
0363-0129
Page Range / eLocation ID:
903 to 923
Subject(s) / Keyword(s):
Mean Field Games, Wasserstein metric, Viscosity Solutions, McKean-Vlasov
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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