{
  "id": "2201.05360",
  "version": "v2",
  "published": "2022-01-14T09:40:52.000Z",
  "updated": "2022-08-03T13:48:20.000Z",
  "title": "Optimal control problems with $L^0(Ω)$ constraints: maximum principle and proximal gradient method",
  "authors": [
    "Daniel Wachsmuth"
  ],
  "categories": [
    "math.OC"
  ],
  "abstract": "We investigate optimal control problems with $L^0$ constraints, which restrict the measure of the support of the controls. We prove necessary optimality conditions of Pontryagin maximum principle type. Here, a special control perturbation is used that respects the $L^0$ constraint. First, the maximum principle is obtained in integral form, which is then turned into a pointwise form. In addition, an optimization algorithm of proximal gradient type is analyzed. Under some assumptions, the sequence of iterates contains strongly converging subsequences, whose limits are feasible and satisfy a subset of the necessary optimality conditions.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2022-08-03T13:48:20.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "optimal control problems",
      "proximal gradient method",
      "contains strongly converging subsequences",
      "constraint",
      "necessary optimality conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}