Volume 29, 2023
|Number of page(s)||38|
|Published online||27 April 2023|
Vanishing viscosity in mean-field optimal control
1 Dipartimento di Matematica “Federigo Enriques”, Università degli Studi di Milano, Via Cesare Saldini 50, 20133 Milano, Italy.
2 Dipartimento di Matematica “Tullio Levi Civita”, Università degli Studi di Padova, Via Trieste 63, 35131 Padova, Italy.
* Corresponding author: email@example.com
Accepted: 26 March 2023
We show the existence of Lipschitz-in-space optimal controls for a class of mean-field control problems with dynamics given by a non-local continuity equation. The proof relies on a vanishing viscosity method: we prove the convergence of the same problem where a diffusion term is added, with a small viscosity parameter.
By using stochastic optimal control, we first show the existence of a sequence of optimal controls for the problem with diffusion. We then build the optimizer of the original problem by letting the viscosity parameter go to zero.
Mathematics Subject Classification: 49J45 / 93E20 / 49J20
Key words: Mean-field equations / optimal control of partial differential equations / vanishing viscosity
© The authors. Published by EDP Sciences, SMAI 2023
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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