{
  "id": "2309.05393",
  "version": "v1",
  "published": "2023-09-11T11:45:58.000Z",
  "updated": "2023-09-11T11:45:58.000Z",
  "title": "Convergence analysis of the semismooth Newton method for sparse control problems governed by semilinear elliptic equations",
  "authors": [
    "Casas Eduardo",
    "Mateos Mariano"
  ],
  "comment": "18 pages",
  "categories": [
    "math.OC"
  ],
  "abstract": "We show that a second order sufficient condition for local optimality, along with a strict complementarity condition, is enough to get the super-linear convergence of the semismooth Newton method for an optimal control problem governed by a semilinear elliptic equation. The objective functional may include a sparsity promoting term and we allow for box control constraints. We also obtain quadratic convergence under quite natural assumptions on the data of the control problem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-09-11T11:45:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J61",
      "49K20",
      "49M15",
      "49M05"
    ],
    "keywords": [
      "semismooth newton method",
      "semilinear elliptic equation",
      "sparse control problems",
      "convergence analysis",
      "second order sufficient condition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}