{
  "id": "2109.11516",
  "version": "v1",
  "published": "2021-09-23T17:39:56.000Z",
  "updated": "2021-09-23T17:39:56.000Z",
  "title": "Weak sharp minima for interval-valued functions and its primal-dual characterizations using generalized Hukuhara subdifferentiability",
  "authors": [
    "Krishan Kumar",
    "Debdas Ghosh",
    "Gourav Kumar"
  ],
  "categories": [
    "math.OC"
  ],
  "abstract": "This article introduces the concept of weak sharp minima (WSM) for convex interval-valued functions (IVFs). To identify a set of WSM of a convex IVF, we provide its primal and dual characterizations. The primal characterization is given in terms of $gH$-directional derivatives. On the other hand, to derive dual characterizations, we propose the notions of the support function of a subset of $I(\\mathbb{R})^{n}$ and $gH$-subdifferentiability for convex IVFs. Further, we develop the required $gH$-subdifferential calculus for convex IVFs. Thereafter, by using the proposed $gH$-subdifferential calculus, we provide dual characterizations for the set of WSM of convex IVFs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-09-23T17:39:56.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "weak sharp minima",
      "generalized hukuhara subdifferentiability",
      "interval-valued functions",
      "convex ivf",
      "primal-dual characterizations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}