Intrinsic Lipschitz Regularity of Mean-Field Optimal Controls

Abstract : In this paper, we provide a sufficient condition for the Lipschitz-in-space regularity for solutions of optimal control problems formulated on continuity equations. Our approach involves a novel combination of mean-field approximation results for infinite-dimensional multi-agent optimal control problems along with an existence result of locally optimal Lipschitz feedbacks. The latter is based in our context on a reformulation of a coercivity estimate in the language of the differential calculus of Wasserstein spaces.
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https://hal.archives-ouvertes.fr/hal-02271059
Contributor : Benoît Bonnet <>
Submitted on : Monday, August 26, 2019 - 3:04:41 PM
Last modification on : Wednesday, August 28, 2019 - 1:20:09 AM

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Benoît Bonnet, Francesco Rossi. Intrinsic Lipschitz Regularity of Mean-Field Optimal Controls. 2019. ⟨hal-02271059⟩

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