{
  "id": "1311.2795",
  "version": "v2",
  "published": "2013-11-12T14:38:28.000Z",
  "updated": "2014-04-16T00:09:43.000Z",
  "title": "Complete solution of a constrained tropical optimization problem with application to location analysis",
  "authors": [
    "Nikolai Krivulin"
  ],
  "comment": "20 pages, 3 figures",
  "journal": "Relational and Algebraic Methods in Computer Science, P. Hoefner, P. Jipsen, W. Kahl, M. E. Mueller, eds., vol. 8428 of Lecture Notes in Computer Science, pp. 362-378, Springer, 2014",
  "doi": "10.1007/978-3-319-06251-8_22",
  "categories": [
    "math.OC",
    "cs.SY"
  ],
  "abstract": "We present a multidimensional optimization problem that is formulated and solved in the tropical mathematics setting. The problem consists of minimizing a nonlinear objective function defined on vectors over an idempotent semifield by means of a conjugate transposition operator, subject to constraints in the form of linear vector inequalities. A complete direct solution to the problem under fairly general assumptions is given in a compact vector form suitable for both further analysis and practical implementation. We apply the result to solve a multidimensional minimax single facility location problem with Chebyshev distance and with inequality constraints imposed on the feasible location area.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-04-16T00:09:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65K10",
      "15A80",
      "65K05",
      "90C48",
      "90B85"
    ],
    "keywords": [
      "constrained tropical optimization problem",
      "complete solution",
      "location analysis",
      "multidimensional minimax single facility location",
      "minimax single facility location problem"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1311.2795K"
    }
  }
}