{
  "id": "1707.03782",
  "version": "v1",
  "published": "2017-07-12T16:11:18.000Z",
  "updated": "2017-07-12T16:11:18.000Z",
  "title": "Valadier-like formulas for the supremum function I",
  "authors": [
    "R. Correa",
    "A. Hantoute",
    "M. A. López"
  ],
  "comment": "27 pages",
  "categories": [
    "math.OC",
    "math.FA"
  ],
  "abstract": "We generalize and improve the original characterization given by Valadier [18, Theorem 1] of the subdifferential of the pointwise supremum of convex functions, involving the subdifferentials of the data functions at nearby points. We remove the continuity assumption made in that work and obtain a general formula for such a subdiferential. In particular, when the supremum is continuous at some point of its domain, but not necessarily at the reference point, we get a simpler version which gives rise to the Valadier formula. Our starting result is the characterization given in [11, Theorem 4], which uses the epsilon-subdifferential at the reference point.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-07-12T16:11:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "26B05",
      "26J25",
      "49H05"
    ],
    "keywords": [
      "supremum function",
      "valadier-like formulas",
      "reference point",
      "data functions",
      "subdifferential"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}