{
  "id": "0901.1821",
  "version": "v3",
  "published": "2009-01-13T16:26:53.000Z",
  "updated": "2011-01-28T13:54:52.000Z",
  "title": "Semidefinite representation of convex hulls of rational varieties",
  "authors": [
    "Didier Henrion"
  ],
  "categories": [
    "math.OC",
    "cs.SY",
    "math.AG"
  ],
  "abstract": "Using elementary duality properties of positive semidefinite moment matrices and polynomial sum-of-squares decompositions, we prove that the convex hull of rationally parameterized algebraic varieties is semidefinite representable (that is, it can be represented as a projection of an affine section of the cone of positive semidefinite matrices) in the case of (a) curves; (b) hypersurfaces parameterized by quadratics; and (c) hypersurfaces parameterized by bivariate quartics; all in an ambient space of arbitrary dimension.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2011-01-28T13:54:52.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "convex hull",
      "semidefinite representation",
      "rational varieties",
      "positive semidefinite moment matrices",
      "polynomial sum-of-squares decompositions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0901.1821H"
    }
  }
}