{
  "id": "2208.03687",
  "version": "v1",
  "published": "2022-08-07T09:34:22.000Z",
  "updated": "2022-08-07T09:34:22.000Z",
  "title": "A Newton derivative scheme for shape optimization problems constrained by variational inequalities",
  "authors": [
    "Nico Goldammer",
    "Volker H. Schulz",
    "Kathrin Welker"
  ],
  "categories": [
    "math.OC"
  ],
  "abstract": "Shape optimization problems constrained by variational inequalities (VI) are non-smooth and non-convex optimization problems. The non-smoothness arises due to the variational inequality constraint, which makes it challenging to derive optimality conditions. Besides the non-smoothness there are complementary aspects due to the VIs as well as distributed, non-linear, non-convex and infinite-dimensional aspects due to the shapes which complicate to set up an optimality system and, thus, to develop fast and higher order solution algorithms. In this paper, we consider Newton-derivatives in order to formulate optimality conditions. In this context, we set up a Newton-shape derivative scheme. Examples show the application of the proposed scheme.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-08-07T09:34:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "49Q10",
      "49J40",
      "35Q93",
      "65K15"
    ],
    "keywords": [
      "shape optimization problems",
      "newton derivative scheme",
      "higher order solution algorithms",
      "variational inequality constraint",
      "formulate optimality conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}