{
  "id": "1402.3095",
  "version": "v1",
  "published": "2014-02-13T11:39:13.000Z",
  "updated": "2014-02-13T11:39:13.000Z",
  "title": "Robust Solutions to Multi-Objective Linear Programs with Uncertain Data",
  "authors": [
    "M. A. Goberna",
    "V. Jeyakumar",
    "G. Li",
    "J. Vicente-Pérez"
  ],
  "comment": "21 pages, Applied mathematics report UNSW",
  "categories": [
    "math.OC"
  ],
  "abstract": "In this paper we examine multi-objective linear programming problems in the face of data uncertainty both in the objective function and the constraints. First, we derive a formula for radius of robust feasibility guaranteeing constraint feasibility for all possible uncertainties within a specified uncertainty set under affine data parametrization. We then present a complete characterization of robust weakly effcient solutions that are immunized against rank one objective matrix data uncertainty. We also provide classes of commonly used constraint data uncertainty sets under which a robust feasible solution of an uncertain multi-objective linear program can be numerically checked whether or not it is a robust weakly efficient solution.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-02-13T11:39:13.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "uncertain data",
      "robust solutions",
      "constraint data uncertainty sets",
      "robust feasibility guaranteeing constraint feasibility",
      "uncertain multi-objective linear program"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1402.3095G"
    }
  }
}