{
  "id": "1710.10187",
  "version": "v1",
  "published": "2017-10-27T15:03:11.000Z",
  "updated": "2017-10-27T15:03:11.000Z",
  "title": "A general representation of delta-normal sets to sublevels of convex functions",
  "authors": [
    "Abderrahim Hantoute",
    "Anton Svensson"
  ],
  "categories": [
    "math.OC",
    "math.FA"
  ],
  "abstract": "The (delta-) normal cone to an arbitrary intersection of sublevel sets of proper, lower semicontinuous, and convex functions is characterized, using either epsilon-subdifferentials at the nominal point or exact subdifferentials at nearby points. Our tools include (epsilon-) calculus rules for sup/max functions. The framework of this work is that of a locally convex space, however, formulas using exact subdifferentials require some restriction either on the space (e.g. Banach), or on the function (e.g. epi-pointed).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-10-27T15:03:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "26B05",
      "26J25",
      "49H05"
    ],
    "keywords": [
      "convex functions",
      "delta-normal sets",
      "general representation",
      "exact subdifferentials",
      "nearby points"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}