{
  "id": "1309.1446",
  "version": "v2",
  "published": "2013-09-05T19:09:03.000Z",
  "updated": "2014-12-20T05:42:52.000Z",
  "title": "Quadratic growth and critical point stability of semi-algebraic functions",
  "authors": [
    "D. Drusvyatskiy",
    "A. D. Ioffe"
  ],
  "comment": "19 pages",
  "categories": [
    "math.OC"
  ],
  "abstract": "We show that quadratic growth of a semi-algebraic function is equivalent to strong metric subregularity of the subdifferential --- a kind of stability of generalized critical points. In contrast, this equivalence can easily fail outside of the semi-algebraic setting. As a consequence, we derive necessary conditions and sufficient conditions for optimality in subdifferential terms.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-09-05T19:09:03.000Z",
      "abstract": "We show that quadratic growth of a semi-algebraic function is equivalent to strong metric subregularity of the subdifferential --- a kind of stability of generalized critical points. In contrast, this equivalence can easily fail outside of the semi-algebraic setting.",
      "comment": "13 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-12-20T05:42:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "49J53",
      "14P10",
      "54C60",
      "65K10",
      "90C31",
      "49J52"
    ],
    "keywords": [
      "critical point stability",
      "quadratic growth",
      "semi-algebraic function",
      "strong metric subregularity",
      "fail outside"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1309.1446D"
    }
  }
}