{
  "id": "1906.09126",
  "version": "v1",
  "published": "2019-06-21T13:16:53.000Z",
  "updated": "2019-06-21T13:16:53.000Z",
  "title": "Restart FISTA with Global Linear Convergence",
  "authors": [
    "Teodoro Alamo",
    "Pablo Krupa",
    "Daniel Limon"
  ],
  "comment": "This paper constitutes an extended and revised version of \"Restart FISTA with Global Linear Convergence\" by Teodoro Alamo, Pablo Krupa and Daniel Limon, presented at the European Control Conference, ECC19, Naples June 2019. (12 pages, 4 figures)",
  "categories": [
    "math.OC"
  ],
  "abstract": "Fast Iterative Shrinking-Threshold Algorithm (FISTA) is a popular fast gradient descent method (FGM) in the field of large scale convex optimization problems. However, it can exhibit undesirable periodic oscillatory behaviour in some applications that slows its convergence. Restart schemes seek to improve the convergence of FGM algorithms by suppressing the oscillatory behaviour. Recently, a restart scheme for FGM has been proposed that provides linear convergence for non strongly convex optimization problems that satisfy a quadratic functional growth condition. However, the proposed algorithm requires prior knowledge of the optimal value of the objective function or of the quadratic functional growth parameter. In this paper we present a restart scheme for FISTA algorithm, with global linear convergence, for non strongly convex optimization problems that satisfy the quadratic growth condition without requiring the aforementioned values. We present some numerical simulations that suggest that the proposed approach outperforms other restart FISTA schemes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-06-21T13:16:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "90C25"
    ],
    "keywords": [
      "global linear convergence",
      "restart fista",
      "non strongly convex optimization problems",
      "fast gradient descent method",
      "scale convex optimization problems"
    ],
    "tags": [
      "conference paper"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}