{
  "id": "1410.0641",
  "version": "v1",
  "published": "2014-10-02T18:52:27.000Z",
  "updated": "2014-10-02T18:52:27.000Z",
  "title": "An inertial forward-backward algorithm for the minimization of the sum of two nonconvex functions",
  "authors": [
    "Radu Ioan Bot",
    "Ernö Robert Csetnek",
    "Szilárd László"
  ],
  "comment": "arXiv admin note: substantial text overlap with arXiv:1406.0724",
  "categories": [
    "math.OC",
    "math.NA"
  ],
  "abstract": "We propose a forward-backward proximal-type algorithm with inertial/memory effects for minimizing the sum of a nonsmooth function with a smooth one in the nonconvex setting. The sequence of iterates generated by the algorithm converges to a critical point of the objective function provided an appropriate regularization of the objective satisfies the Kurdyka-\\L{}ojasiewicz inequality, which is for instance fulfilled for semi-algebraic functions. We illustrate the theoretical results by considering two numerical experiments: the first one concerns the ability of recovering the local optimal solutions of nonconvex optimization problems, while the second one refers to the restoration of a noisy blurred image.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-10-02T18:52:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "90C26",
      "90C30",
      "65K10"
    ],
    "keywords": [
      "inertial forward-backward algorithm",
      "nonconvex functions",
      "minimization",
      "local optimal solutions",
      "nonconvex optimization problems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1410.0641I"
    }
  }
}