| Issue |
ESAIM: COCV
Volume 29, 2023
|
|
|---|---|---|
| Article Number | 29 | |
| Number of page(s) | 38 | |
| DOI | https://doi.org/10.1051/cocv/2023024 | |
| 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: gennaro.ciampa@unimi.it
Received:
3
March
2023
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.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.