{
  "id": "1506.02253",
  "version": "v1",
  "published": "2015-06-07T11:35:28.000Z",
  "updated": "2015-06-07T11:35:28.000Z",
  "title": "Existence, Pareto reducibility, and connectedness in multi-objective optimization: Elementary proofs and extension",
  "authors": [
    "Latif Pourkarimi",
    "Majid Soleimani-damaneh"
  ],
  "categories": [
    "math.OC"
  ],
  "abstract": "This paper is divided to two parts. In the first part, we provide elementary proofs for some important results in multi-objective optimization. The given proofs are so simple and short in compared to the existing ones. Also, a Pareto reducibility result is extended from efficiency to proper efficiency. The second part is devoted to the connections between nonemptiness, $R^p_{\\geqq}$-(semi)compactness, external stability and connectedness of the set of nondominated solutions in multi-objective optimization. Furthermore, it is shown that some assumption in an important result, concerning connectedness, is redundant and should be removed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-06-07T11:35:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "90B50"
    ],
    "keywords": [
      "multi-objective optimization",
      "elementary proofs",
      "connectedness",
      "important result",
      "pareto reducibility result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150602253P"
    }
  }
}