{
  "id": "1309.5508",
  "version": "v3",
  "published": "2013-09-21T18:05:08.000Z",
  "updated": "2016-09-14T23:29:18.000Z",
  "title": "Pareto optimality conditions and duality for vector quadratic fractional optimization problems",
  "authors": [
    "Washington Alves de Oliveira",
    "Antonio Beato Moreno",
    "Antonio Carlos Moretti",
    "Luiz Leduino de Salles Neto"
  ],
  "comment": "22 pages",
  "journal": "Journal of Applied Mathematics; Volume 2014, Article ID 983643, 13 pages",
  "doi": "10.1155/2014/983643",
  "categories": [
    "math.OC"
  ],
  "abstract": "One of the most important optimality conditions to aid to solve a vector optimization problem is the first-order necessary optimality condition that generalizes the Karush-Kuhn-Tucker condition. However, to obtain the sufficient optimality conditions, it is necessary to impose additional assumptions on the objective functions and in the constraint set. The present work is concerned with the constrained vector quadratic fractional optimization problem. It shows that sufficient Pareto optimality conditions and the main duality theorems can be established without the assumption of generalized convexity in the objective functions, by considering some assumptions on a linear combination of Hessian matrices instead. The main aspect of this contribution is the development of Pareto optimality conditions based on a similar second-order sufficient condition for problems with convex constraints, without convexity assumptions on the objective functions. These conditions might be useful to determine termination criteria in the development of algorithms.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-08-08T16:42:07.000Z",
      "comment": "22 pages. To appear in Journal of Applied Mathematics (in press)",
      "journal": null,
      "doi": null,
      "authors": [
        "Washington Alves de Oliveira",
        "Antonio Beato Moreno",
        "Antônio Carlos Moretti",
        "Luiz Leduíno de Salles Neto"
      ]
    },
    {
      "version": "v3",
      "updated": "2016-09-14T23:29:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "90C29",
      "G.1.6"
    ],
    "keywords": [
      "vector quadratic fractional optimization problem",
      "objective functions",
      "sufficient pareto optimality conditions",
      "assumption"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Hindawi",
      "journal": "Adv. High Energ. Phys."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1309.5508A"
    }
  }
}