{
  "id": "2305.06765",
  "version": "v1",
  "published": "2023-05-11T12:42:05.000Z",
  "updated": "2023-05-11T12:42:05.000Z",
  "title": "Multiplier rules for Dini-derivatives in a topological vector space",
  "authors": [
    "Mohammed Bachir",
    "Rongzhen Lyu"
  ],
  "categories": [
    "math.OC"
  ],
  "abstract": "We provide new results of first-order necessary conditions of optimality problem in the form of John's theorem and in the form of Karush-Kuhn-Tucker's theorem. We establish our result in a topological vector space for problems with inequality constraints and in a Banach space for problems with equality and inequality constraints. Our contributions consist in the extension of the results known for the Fr\\'echet and Gateaux-differentiable functions as well as for the Clarke's subdifferential of Lipschitz functions, to the more general Dini-differentiable functions. As consequences, we extend the result of B.H. Pourciau in \\cite[Theorem 6, p. 445]{Po} from the convexity to the {\\it \"Dini-pseudoconvexity\"}.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-05-11T12:42:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "90C30",
      "49K99",
      "90C48"
    ],
    "keywords": [
      "topological vector space",
      "multiplier rules",
      "dini-derivatives",
      "inequality constraints",
      "first-order necessary conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}