{
  "id": "1401.6509",
  "version": "v2",
  "published": "2014-01-25T09:16:40.000Z",
  "updated": "2014-10-01T15:58:31.000Z",
  "title": "Linear Convergence of the Douglas-Rachford Method for Two Closed Sets",
  "authors": [
    "Hung M. Phan"
  ],
  "categories": [
    "math.OC",
    "math.NA"
  ],
  "abstract": "In this paper, we investigate the Douglas-Rachford method for two closed (possibly nonconvex) sets in Euclidean spaces. We show that under certain regularity conditions, the Douglas-Rachford method converges locally with R-linear rate. In convex settings, we prove that the linear convergence is global. Our study recovers recent results on the same topic.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-01-25T09:16:40.000Z",
      "abstract": "In this paper, we investigate the Douglas-Rachford method for two closed (possibly nonconvex) sets in Euclidean spaces. We introduce the stationary and stationary-projected sets for operators. The new tools provide useful properties, which assist the study of the method. In particular, we show that under the restricted constraint qualification condition and set regularity conditions, the Douglas-Rachford method converges locally with linear rate. In convex settings, we prove that the linear convergence is global. Our study recovers recent results on the same topic.",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-10-01T15:58:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "49M27",
      "65K10",
      "47H09",
      "49J52",
      "49M20",
      "49M37",
      "65K05",
      "90C26",
      "90C30"
    ],
    "keywords": [
      "linear convergence",
      "closed sets",
      "set regularity conditions",
      "restricted constraint qualification condition",
      "convex settings"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1401.6509P"
    }
  }
}