{
  "id": "1203.1493",
  "version": "v2",
  "published": "2012-03-07T15:13:08.000Z",
  "updated": "2014-03-14T17:48:15.000Z",
  "title": "A Riemannian View on Shape Optimization",
  "authors": [
    "Volker Schulz"
  ],
  "comment": "15 pages, 1 figure, 1 table. Forschungsbericht / Universit\\\"at Trier, Mathematik, Informatik 2012, 1",
  "journal": "Foundations of Computational Mathematics, 14:483-501, 2014",
  "doi": "10.1007/s10208-014-9200-5",
  "categories": [
    "math.OC"
  ],
  "abstract": "Shape optimization based on the shape calculus is numerically mostly performed by means of steepest descent methods. This paper provides a novel framework to analyze shape-Newton optimization methods by exploiting a Riemannian perspective. A Riemannian shape Hessian is defined yielding often sought properties like symmetry and quadratic convergence for Newton optimization methods.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-03-14T17:48:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "49Q10",
      "49M15",
      "53B20"
    ],
    "keywords": [
      "shape optimization",
      "riemannian view",
      "analyze shape-newton optimization methods",
      "riemannian shape hessian",
      "steepest descent methods"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1203.1493S"
    }
  }
}