{
  "id": "2309.07554",
  "version": "v1",
  "published": "2023-09-14T09:36:51.000Z",
  "updated": "2023-09-14T09:36:51.000Z",
  "title": "Bilinear control of semilinear elliptic PDEs: Convergence of a semismooth Newton method",
  "authors": [
    "Eduardo Casas",
    "Konstantinos Chrysafinos",
    "Mariano Mateos"
  ],
  "categories": [
    "math.OC"
  ],
  "abstract": "In this paper, we carry out the analysis of the semismooth Newton method for bilinear control problems related to semilinear elliptic PDEs. We prove existence, uniqueness and regularity for the solution of the state equation, as well as differentiability properties of the control to state mapping. Then, first and second order optimality conditions are obtained. Finally, we prove the superlinear convergence of the semismooth Newton method to local solutions satisfying no-gap second order sufficient optimality conditions as well as a strict complementarity condition.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-09-14T09:36:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J61",
      "49K20",
      "49M15",
      "49M05"
    ],
    "keywords": [
      "semismooth newton method",
      "semilinear elliptic pdes",
      "bilinear control",
      "order sufficient optimality conditions",
      "no-gap second order sufficient"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}