{
  "id": "2103.13270",
  "version": "v1",
  "published": "2021-03-24T15:38:37.000Z",
  "updated": "2021-03-24T15:38:37.000Z",
  "title": "Semi-definite representations for sets of cubics on the 2-sphere",
  "authors": [
    "Roland Hildebrand"
  ],
  "categories": [
    "math.OC",
    "math.CA"
  ],
  "abstract": "The compact set of homogeneous quadratic polynomials in $n$ real variables with modulus bounded by 1 on the unit sphere $S^{n-1}$ is trivially semi-definite representable. The compact set of homogeneous ternary quartics with modulus bounded by 1 on the unit sphere $S^2$ is also semi-definite representable. This suggests that the compact set of homogeneous ternary cubics with modulus bounded by 1 on $S^2$ is semi-definite representable. We deduce an explicit semi-definite representation of this norm ball. More generally, we provide a semi-definite description of the cone of inhomogeneous ternary cubics which are nonnegative on $S^2$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-03-24T15:38:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "90C22",
      "90C23"
    ],
    "keywords": [
      "compact set",
      "semi-definite representable",
      "unit sphere",
      "explicit semi-definite representation",
      "inhomogeneous ternary cubics"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}