{
  "id": "2212.04541",
  "version": "v1",
  "published": "2022-12-08T20:06:21.000Z",
  "updated": "2022-12-08T20:06:21.000Z",
  "title": "A technical note on \"The KKT Optimality Conditions For Optimization Problem With Interval-Valued Objective Function On Hadamard Manifolds\"",
  "authors": [
    "Hilal Ahmad Bhat",
    "Akhlad Iqbal"
  ],
  "categories": [
    "math.OC",
    "math.DG"
  ],
  "abstract": "In this technical note, we disprove S.-L. Chen's \\cite{chen} assertion that the generalized Hukuhara directional differentiability of an interval-valued function defined on a Hadamard manifold is fully identical to the directional differentiability of its endpoint functions by providing a counterexample. Moreover, we address imprecisions in several results proved by using the aforementioned assertion in \\cite{chen}. We provide correct statements of the imprecise results and construct examples in their support.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-12-08T20:06:21.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "kkt optimality conditions",
      "hadamard manifold",
      "interval-valued objective function",
      "technical note",
      "optimization problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}