{
  "id": "2002.04921",
  "version": "v1",
  "published": "2020-02-12T11:20:15.000Z",
  "updated": "2020-02-12T11:20:15.000Z",
  "title": "Analysis of Optimal Control Problems with an $L^0$ Term in the Cost Functional",
  "authors": [
    "Eduardo Casas",
    "Daniel Wachsmuth"
  ],
  "categories": [
    "math.OC"
  ],
  "abstract": "In this paper, we investigate optimal control problems subject to a semilinear elliptic partial differential equations. The cost functional contains a term that measures the size of the support of the control, which is the so-called $L^0$-norm. We provide necessary and sufficient optimality conditions of second-order. The sufficient second-order condition is obtained by analyzing a partially convexified problem. Interestingly, the structure of the problem yields second-order conditions with different bilinear forms for the necessary and for the sufficient condition.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-02-12T11:20:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J61",
      "49K20",
      "40J52"
    ],
    "keywords": [
      "cost functional",
      "semilinear elliptic partial differential equations",
      "problem yields second-order conditions",
      "optimal control problems subject",
      "sufficient second-order condition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}