{
  "id": "1711.06570",
  "version": "v1",
  "published": "2017-11-16T14:28:15.000Z",
  "updated": "2017-11-16T14:28:15.000Z",
  "title": "Approaching nonsmooth nonconvex minimization through second order proximal-gradient dynamical systems",
  "authors": [
    "Radu Ioan Bot",
    "Ernö Robert Csetnek",
    "Szilárd Csaba László"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:1507.01416, arXiv:1610.00911, arXiv:1703.01339",
  "categories": [
    "math.OC",
    "math.DS"
  ],
  "abstract": "We investigate the asymptotic properties of the trajectories generated by a second-order dynamical system of proximal-gradient type stated in connection with the minimization of the sum of a nonsmooth convex and a (possibly nonconvex) smooth function. The convergence of the generated trajectory to a critical point of the objective is ensured provided a regularization of the objective function satisfies the Kurdyka-\\L{}ojasiewicz property. We also provide convergence rates for the trajectory formulated in terms of the \\L{}ojasiewicz exponent.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-11-16T14:28:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "34G25",
      "47J25",
      "47H05",
      "90C26",
      "90C30",
      "65K10"
    ],
    "keywords": [
      "second order proximal-gradient dynamical systems",
      "approaching nonsmooth nonconvex minimization",
      "trajectory"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}