{
  "id": "2111.13015",
  "version": "v2",
  "published": "2021-11-25T10:53:36.000Z",
  "updated": "2023-04-27T08:19:59.000Z",
  "title": "Vanishing viscosity in mean-field optimal control",
  "authors": [
    "Gennaro Ciampa",
    "Francesco Rossi"
  ],
  "journal": "ESAIM: COCV 29 (2023) 29",
  "doi": "10.1051/cocv/2023024",
  "categories": [
    "math.OC",
    "math.AP"
  ],
  "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.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2023-04-27T08:19:59.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "mean-field optimal control",
      "vanishing viscosity",
      "mean-field control problems",
      "non-local continuity equation",
      "small viscosity parameter"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}