{
  "id": "math/0311017",
  "version": "v3",
  "published": "2003-11-03T11:09:48.000Z",
  "updated": "2005-10-11T11:46:49.000Z",
  "title": "Radii minimal projections of polytopes and constrained optimization of symmetric polynomials",
  "authors": [
    "Rene Brandenberg",
    "Thorsten Theobald"
  ],
  "comment": "Minor revisions. To appear in Advances in Geometry",
  "categories": [
    "math.MG",
    "math.CO"
  ],
  "abstract": "We provide a characterization of the radii minimal projections of polytopes onto $j$-dimensional subspaces in Euclidean space $\\E^n$. Applied on simplices this characterization allows to reduce the computation of an outer radius to a computation in the circumscribing case or to the computation of an outer radius of a lower-dimensional simplex. In the second part of the paper, we use this characterization to determine the sequence of outer $(n-1)$-radii of regular simplices (which are the radii of smallest enclosing cylinders). This settles a question which arose from the incidence that a paper by Wei{\\ss}bach (1983) on this determination was erroneous. In the proof, we first reduce the problem to a constrained optimization problem of symmetric polynomials and then to an optimization problem in a fixed number of variables with additional integer constraints.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2005-10-11T11:46:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "51N20",
      "52A15",
      "52B12",
      "52B55",
      "68W30"
    ],
    "keywords": [
      "radii minimal projections",
      "symmetric polynomials",
      "constrained optimization",
      "optimization problem",
      "outer radius"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math.....11017B"
    }
  }
}