Vanishing viscosity in mean-field optimal control
Optimization and Control
2023-04-28 v2 Analysis of PDEs
Abstract
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.
Cite
@article{arxiv.2111.13015,
title = {Vanishing viscosity in mean-field optimal control},
author = {Gennaro Ciampa and Francesco Rossi},
journal= {arXiv preprint arXiv:2111.13015},
year = {2023}
}