{
  "id": "2209.10670",
  "version": "v1",
  "published": "2022-09-21T21:48:15.000Z",
  "updated": "2022-09-21T21:48:15.000Z",
  "title": "Multi-Degrees in Polynomial Optimization",
  "authors": [
    "Kemal Rose"
  ],
  "categories": [
    "math.OC",
    "math.AG"
  ],
  "abstract": "We study structured optimization problems with polynomial objective function and polynomial equality constraints. The structure comes from a multi-grading on the polynomial ring in several variables. For fixed multi-degrees we determine the generic number of complex critical points. This serves as a measure for the algebraic complexity of the optimization problem. We also discuss computation and certification methods coming from numerical nonlinear algebra.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-09-21T21:48:15.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "polynomial optimization",
      "study structured optimization problems",
      "polynomial equality constraints",
      "generic number",
      "complex critical points"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}