{
  "id": "2211.10942",
  "version": "v1",
  "published": "2022-11-20T10:37:26.000Z",
  "updated": "2022-11-20T10:37:26.000Z",
  "title": "On the convergence analysis of DCA",
  "authors": [
    "Yi-Shuai Niu"
  ],
  "categories": [
    "math.OC",
    "cs.NA",
    "math.NA"
  ],
  "abstract": "In this paper, we propose a clean and general proof framework to establish the convergence analysis of the Difference-of-Convex (DC) programming algorithm (DCA) for both standard DC program and convex constrained DC program. We first discuss suitable assumptions for the well-definiteness of DCA. Then, we focus on the convergence analysis of DCA, in particular, the global convergence of the sequence $\\{x^k\\}$ generated by DCA under the Lojasiewicz subgradient inequality and the Kurdyka-Lojasiewicz property respectively. Moreover, the convergence rate for the sequences $\\{f(x^k)\\}$ and $\\{\\|x^k-x^*\\|\\}$ are also investigated. We hope that the proof framework presented in this article will be a useful tool to conveniently establish the convergence analysis for many variants of DCA and new DCA-type algorithms.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-11-20T10:37:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "90C26",
      "90C30",
      "65K05"
    ],
    "keywords": [
      "convergence analysis",
      "general proof framework",
      "lojasiewicz subgradient inequality",
      "standard dc program",
      "convex constrained dc program"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}