{
  "id": "1812.00558",
  "version": "v1",
  "published": "2018-12-03T05:14:16.000Z",
  "updated": "2018-12-03T05:14:16.000Z",
  "title": "Metric Subregularity of Subdifferential and KL Property of Exponent 1/2",
  "authors": [
    "Shaohua Pan",
    "Dongdong Zhang",
    "Yulan Liu"
  ],
  "comment": "16 pages",
  "categories": [
    "math.OC"
  ],
  "abstract": "For a proper lower semicontinuous function, we study the relations between the metric subregularity of its limiting subdifferential relative to the critical set and the KL property of exponent 1/2. When the function is convex, we establish the equivalence between them. When the function is nonconvex, we show that the KL property of exponent 1/2 along with the quadratic growth on the critical set implies the metric subregularity of the subdifferential relative to the critical set; and if the function is primal-lower-nice, under an assumption on stationary values, the latter implies the former. These results provide a bridge for the two kinds of regularity and contribute to enriching each other.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-12-03T05:14:16.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "kl property",
      "metric subregularity",
      "proper lower semicontinuous function",
      "subdifferential relative",
      "quadratic growth"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}