{
  "id": "2308.09556",
  "version": "v1",
  "published": "2023-08-18T13:39:29.000Z",
  "updated": "2023-08-18T13:39:29.000Z",
  "title": "A Principle for Global Optimization with Gradients",
  "authors": [
    "Nils Müller"
  ],
  "comment": "16 pages, 3 figures",
  "categories": [
    "math.OC",
    "cs.NA",
    "cs.NE",
    "math.NA",
    "stat.ML"
  ],
  "abstract": "This work demonstrates the utility of gradients for the global optimization of certain differentiable functions with many suboptimal local minima. To this end, a principle for generating search directions from non-local quadratic approximants based on gradients of the objective function is analyzed. Experiments measure the quality of non-local search directions as well as the performance of a proposed simplistic algorithm, of the covariance matrix adaptation evolution strategy (CMA-ES), and of a randomly reinitialized Broyden-Fletcher-Goldfarb-Shanno (BFGS) method.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-08-18T13:39:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "90C26",
      "90C15",
      "90C53",
      "G.1.6"
    ],
    "keywords": [
      "global optimization",
      "covariance matrix adaptation evolution strategy",
      "non-local search directions",
      "non-local quadratic approximants",
      "suboptimal local minima"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}