{
  "id": "1609.03626",
  "version": "v1",
  "published": "2016-09-12T22:55:14.000Z",
  "updated": "2016-09-12T22:55:14.000Z",
  "title": "Convergence Rates of Inertial Splitting Schemes for Nonconvex Composite Optimization",
  "authors": [
    "Patrick R. Johnstone",
    "Pierre Moulin"
  ],
  "categories": [
    "math.OC"
  ],
  "abstract": "We study the convergence properties of a general inertial first-order proximal splitting algorithm for solving nonconvex nonsmooth optimization problems. Using the Kurdyka--\\L ojaziewicz (KL) inequality we establish new convergence rates which apply to several inertial algorithms in the literature. Our basic assumption is that the objective function is semialgebraic, which lends our results broad applicability in the fields of signal processing and machine learning. The convergence rates depend on the exponent of the \"desingularizing function\" arising in the KL inequality. Depending on this exponent, convergence may be finite, linear, or sublinear and of the form $O(k^{-p})$ for $p>1$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-09-12T22:55:14.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "convergence rates",
      "nonconvex composite optimization",
      "inertial splitting schemes",
      "nonconvex nonsmooth optimization problems",
      "first-order proximal splitting algorithm"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}