{
  "id": "1210.4770",
  "version": "v1",
  "published": "2012-10-17T15:34:02.000Z",
  "updated": "2012-10-17T15:34:02.000Z",
  "title": "A new algebraic solution to multidimensional minimax location problems with Chebyshev distance",
  "authors": [
    "Nikolai Krivulin"
  ],
  "comment": "ISSN 2224-2880",
  "journal": "WSEAS Transactions on Mathematics, 2012, Vol. 11, no. 7, pp. 605-614",
  "categories": [
    "math.OC"
  ],
  "abstract": "Both unconstrained and constrained minimax single facility location problems are considered in multidimensional space with Chebyshev distance. A new solution approach is proposed within the framework of idempotent algebra to reduce the problems to solving linear vector equations and minimizing functionals defined on some idempotent semimodule. The approach offers a solution in a closed form that actually involves performing matrix-vector multiplications in terms of idempotent algebra for appropriate matrices and vectors. To illustrate the solution procedures, numerical and graphical examples of two-dimensional problems are given.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-10-17T15:34:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65K05",
      "15A80",
      "90C08",
      "12K10",
      "90B85"
    ],
    "keywords": [
      "multidimensional minimax location problems",
      "chebyshev distance",
      "algebraic solution",
      "minimax single facility location problems",
      "constrained minimax single facility location"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1210.4770K"
    }
  }
}