{
  "id": "2002.07154",
  "version": "v1",
  "published": "2020-02-16T08:06:53.000Z",
  "updated": "2020-02-16T08:06:53.000Z",
  "title": "A forward-backward algorithm with different inertial terms for the minimization of the sum of two non-convex functions",
  "authors": [
    "Szilárd Csaba László"
  ],
  "comment": "21 pages. arXiv admin note: substantial text overlap with arXiv:1811.09616",
  "categories": [
    "math.FA",
    "math.OC"
  ],
  "abstract": "We investigate an inertial forward-backward algorithm in connection with the minimization of the sum of a non-smooth and possible non-convex and a non-convex differentiable function. The algorithm is formulated in the spirit of the famous FISTA method, however the setting is non-convex and we allow different inertial terms. We also treat the case when the non-smooth function is convex and we show that in this case a better step-size can be allowed. We prove some abstract convergence results which applied to our numerical scheme allow us to show that the generated sequences converge to a critical point of the objective function, provided a regularization of the objective function satisfies the Kurdyka-{\\L}ojasiewicz property.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-02-16T08:06:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "90C26",
      "90C30",
      "65K10"
    ],
    "keywords": [
      "inertial terms",
      "non-convex functions",
      "minimization",
      "abstract convergence results",
      "non-convex differentiable function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}