{
  "id": "1311.4989",
  "version": "v2",
  "published": "2013-11-20T09:37:29.000Z",
  "updated": "2014-06-23T12:01:59.000Z",
  "title": "Classical and strong convexity of sublevel sets and application to attainable sets of nonlinear systems",
  "authors": [
    "Alexander Weber",
    "Gunther Reissig"
  ],
  "comment": "20 pages, 3 figures",
  "categories": [
    "math.OC"
  ],
  "abstract": "Necessary and sufficient conditions for convexity and strong convexity, respectively, of sublevel sets that are defined by finitely many real-valued $C^{1,1}$-maps are presented. A novel characterization of strongly convex sets in terms of the so-called local quadratic support is proved. The results concerning strong convexity are used to derive sufficient conditions for attainable sets of continuous-time nonlinear systems to be strongly convex. An application of these conditions is a novel method to over-approximate attainable sets when strong convexity is present.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-06-23T12:01:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52A30",
      "52A20",
      "93C10",
      "93C15"
    ],
    "keywords": [
      "attainable sets",
      "sublevel sets",
      "application",
      "sufficient conditions",
      "continuous-time nonlinear systems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1311.4989W"
    }
  }
}