{
  "id": "1511.09438",
  "version": "v1",
  "published": "2015-11-30T19:40:21.000Z",
  "updated": "2015-11-30T19:40:21.000Z",
  "title": "Higher-Order Optimality Conditions in Unconstrained Optimization with an Arbitrary Nondifferentiable Function",
  "authors": [
    "Vsevolod I. Ivanov"
  ],
  "comment": "7 pages. arXiv admin note: substantial text overlap with arXiv:1311.2367",
  "categories": [
    "math.OC"
  ],
  "abstract": "In this paper, we introduce a new higher-order directional derivative and higher-order subdifferential of Hadamard type of a given proper extended real function. This derivative is consistent with the classical higher-order Fr\\'echet directional derivative in the sense that both derivatives of the same order coincide if the last one exists. We obtain necessary and sufficient conditions of order $n$ ($n$ is a positive integer) for a local minimum and isolated local minimum of order $n$ in terms of these derivatives and subdifferentials. We do not require any restrictions on the function in our results.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-11-30T19:40:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "49K10",
      "90C46",
      "26B05",
      "26B25"
    ],
    "keywords": [
      "higher-order optimality conditions",
      "arbitrary nondifferentiable function",
      "unconstrained optimization",
      "higher-order frechet directional derivative",
      "local minimum"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151109438I"
    }
  }
}