{
  "id": "1904.02772",
  "version": "v1",
  "published": "2019-04-04T20:03:11.000Z",
  "updated": "2019-04-04T20:03:11.000Z",
  "title": "Directional quasi/pseudo-normality as sufficient conditions for metric subregularity",
  "authors": [
    "Kuang Bai",
    "Jane Ye",
    "Jin Zhang"
  ],
  "categories": [
    "math.OC"
  ],
  "abstract": "In this paper we study sufficient conditions for metric subregularity of a set-valued map which is the sum of a single-valued continuous map and a locally closed subset. First we derive a sufficient condition for metric subregularity which is weaker than the so-called first-order sufficient condition for metric subregularity (FOSCMS) by adding an extra sequential condition. Then we introduce a directional version of the quasi-normality and the pseudo-normality which is stronger than the new {weak} sufficient condition for metric subregularity but is weaker than the classical quasi-normality and pseudo-normality respectively. Moreover we introduce a nonsmooth version of the second-order sufficient condition for metric subregularity and show that it is a sufficient condition for the new sufficient condition for metric {sub}regularity to hold. An example is used to illustrate that the directional pseduo-normality can be weaker than FOSCMS. For the class of set-valued maps where the single-valued mapping is affine and the abstract set is the union of finitely many convex polyhedral sets, we show that the pseudo-normality and hence the directional pseudo-normality holds automatically at each point of the graph. Finally we apply our results to the complementarity and the Karush-Kuhn-Tucker systems.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-04-04T20:03:11.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "metric subregularity",
      "directional quasi/pseudo-normality",
      "first-order sufficient condition",
      "extra sequential condition",
      "set-valued map"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}