{
  "id": "1606.09070",
  "version": "v1",
  "published": "2016-06-29T13:00:00.000Z",
  "updated": "2016-06-29T13:00:00.000Z",
  "title": "Local Convergence of the Heavy-ball Method and iPiano for Non-convex Optimization",
  "authors": [
    "Peter Ochs"
  ],
  "categories": [
    "math.OC"
  ],
  "abstract": "A local convergence result for abstract descent methods is proved. The sequence of iterates is attracted by a local (or global) minimum, stays in its neighborhood and converges. This result allows algorithms to exploit local properties of the objective function: The gradient of the Moreau envelope of a prox-regular functions is locally Lipschitz continuous and expressible in terms of the proximal mapping. We apply these results to establish relations between an inertial forward--backward splitting method (iPiano) and inertial averaged/alternating proximal minimization.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-06-29T13:00:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "90C26",
      "90C30",
      "65K05"
    ],
    "keywords": [
      "non-convex optimization",
      "heavy-ball method",
      "local convergence result",
      "abstract descent methods",
      "inertial averaged/alternating proximal minimization"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}