{
  "id": "1909.01123",
  "version": "v1",
  "published": "2019-09-03T12:49:50.000Z",
  "updated": "2019-09-03T12:49:50.000Z",
  "title": "Continuous optimization",
  "authors": [
    "Xiaopeng Luo",
    "Xin Xu"
  ],
  "comment": "18 pages, 5 figures",
  "categories": [
    "math.OC",
    "cs.CC",
    "cs.NA",
    "math.NA"
  ],
  "abstract": "Sufficient conditions for the existence of efficient algorithms are established by introducing the concept of contractility for continuous optimization. Then all the possible continuous problems are divided into three categories: contractile in logarithmic time, contractile in polynomial time, or noncontractile. For the first two, we propose an efficient contracting algorithm to find the set of all global minimizers with a theoretical guarantee of linear convergence; for the last one, we discuss possible troubles caused by using the proposed algorithm.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-09-03T12:49:50.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "continuous optimization",
      "sufficient conditions",
      "global minimizers",
      "efficient algorithms",
      "efficient contracting algorithm"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}