{
  "id": "2403.01135",
  "version": "v1",
  "published": "2024-03-02T08:29:23.000Z",
  "updated": "2024-03-02T08:29:23.000Z",
  "title": "Semismooth Newton Method for Boundary Bilinear Control",
  "authors": [
    "Eduardo Casas",
    "Konstantinos Chrysafinos",
    "Mariano Mateos"
  ],
  "journal": "IEEE Control Systems Letters, 7 (2023) 3549--3554",
  "doi": "10.1109/LCSYS.2023.3337747",
  "categories": [
    "math.OC"
  ],
  "abstract": "We study a control-constrained optimal control problem governed by a semilinear elliptic equation. The control acts in a bilinear way on the boundary, and can be interpreted as a heat transfer coefficient. A detailed study of the state equation is performed and differentiability properties of the control-to-state mapping are shown. First and second order optimality conditions are derived. Our main result is the proof of 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": "2024-03-02T08:29:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J61",
      "49K20",
      "49M15",
      "49M05"
    ],
    "keywords": [
      "semismooth newton method",
      "boundary bilinear control",
      "order sufficient optimality conditions",
      "no-gap second order sufficient",
      "second order sufficient optimality"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "IEEE"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}