{
  "id": "0907.5439",
  "version": "v5",
  "published": "2009-07-31T18:43:19.000Z",
  "updated": "2010-12-30T14:52:02.000Z",
  "title": "Generalized differentiation with positively homogeneous maps: Applications in set-valued analysis and metric regularity",
  "authors": [
    "C. H. Jeffrey Pang"
  ],
  "comment": "This submission corrects errors from the previous version after referees' comments. Changes are in Proposition 2.4, Proposition 4.12, and Sections 7 and 8",
  "categories": [
    "math.OC"
  ],
  "abstract": "We propose a new concept of generalized differentiation of set-valued maps that captures the first order information. This concept encompasses the standard notions of Frechet differentiability, strict differentiability, calmness and Lipschitz continuity in single-valued maps, and the Aubin property and Lipschitz continuity in set-valued maps. We present calculus rules, sharpen the relationship between the Aubin property and coderivatives, and study how metric regularity and open covering can be refined to have a directional property similar to our concept of generalized differentiation. Finally, we discuss the relationship between the robust form of generalization differentiation and its one sided counterpart.",
  "revisions": [
    {
      "version": "v5",
      "updated": "2010-12-30T14:52:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "26E25",
      "46G05",
      "46T20",
      "47H04",
      "49J50",
      "49J52",
      "49J53",
      "54C05",
      "54C50",
      "54C60",
      "58C06",
      "58C07",
      "58C20",
      "58C25",
      "90C31"
    ],
    "keywords": [
      "generalized differentiation",
      "positively homogeneous maps",
      "metric regularity",
      "set-valued analysis",
      "applications"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0907.5439P"
    }
  }
}