{
  "id": "2104.14750",
  "version": "v1",
  "published": "2021-04-30T04:21:57.000Z",
  "updated": "2021-04-30T04:21:57.000Z",
  "title": "A Refined Inertial DCA for DC Programming",
  "authors": [
    "Yu You",
    "Yi-Shuai Niu"
  ],
  "comment": "27 pages, 5 figures",
  "categories": [
    "math.OC",
    "cs.CV"
  ],
  "abstract": "We consider the difference-of-convex (DC) programming problems whose objective function is level-bounded. The classical DC algorithm (DCA) is well-known for solving this kind of problems, which returns a critical point. Recently, de Oliveira and Tcheo incorporated the inertial-force procedure into DCA (InDCA) for potential acceleration and preventing the algorithm from converging to a critical point which is not d(directional)-stationary. In this paper, based on InDCA, we propose two refined inertial DCA (RInDCA) with enlarged inertial step-sizes for better acceleration. We demonstrate the subsequential convergence of our refined versions to a critical point. In addition, by assuming the Kurdyka-Lojasiewicz (KL) property of the objective function, we establish the sequential convergence of RInDCA. Numerical simulations on image restoration problem show the benefit of enlarged step-size.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-04-30T04:21:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "90C26",
      "90C30",
      "68U10"
    ],
    "keywords": [
      "refined inertial dca",
      "dc programming",
      "critical point",
      "objective function",
      "image restoration problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}