{
  "id": "2104.11167",
  "version": "v1",
  "published": "2021-04-22T16:36:33.000Z",
  "updated": "2021-04-22T16:36:33.000Z",
  "title": "Ekeland's Variational Principle for Interval-valued Functions",
  "authors": [
    "Gourav Kumar",
    "Debdas Ghosh"
  ],
  "categories": [
    "math.OC"
  ],
  "abstract": "In this paper, we attempt to propose Ekeland's variational principle for interval-valued functions (IVFs). To develop the variational principle, we study the concept of sequence of intervals. In the sequel, the idea of gH-semicontinuity for IVFs is explored. A necessary and sufficient condition for an IVF to be gH-continuous in terms of gH-lower and upper semicontinuity is given. Moreover, we prove a characterization for gH-lower semicontinuity by the level sets of the IVF. With the help of this characterization result, we ensure the existence of a minimum for an extended gH-lower semicontinuous, level-bounded and proper IVF. To find an approximate minima of a gH-lower semicontinuous and gH-Gateaux differentiable IVF, the proposed Ekeland's variational principle is used.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-04-22T16:36:33.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "ekelands variational principle",
      "interval-valued functions",
      "characterization result",
      "gh-lower semicontinuity",
      "upper semicontinuity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}