{
  "id": "1805.09077",
  "version": "v1",
  "published": "2018-05-23T12:04:30.000Z",
  "updated": "2018-05-23T12:04:30.000Z",
  "title": "Accelerating the Fast Gradient Method",
  "authors": [
    "Ross Drummond",
    "Stephen Duncan"
  ],
  "comment": "8 pages. 6 figures",
  "categories": [
    "math.OC"
  ],
  "abstract": "A set of accelerated first order optimisation algorithms for minimising strictly convex functions are proposed. Using only gradient information, these algorithms can achieve a worst-case convergence rate proportional to $ 1-\\left(\\frac{\\mu}{L}\\right)^{1/N}$ for $N = 1, 2, 3, \\dots$ and can exceed that of the fast gradient method. However, the improvement in the rate of convergence comes at the expense of a loss of robustness. Robustness is recovered by using an adaptive restarting controller that guarantees iterate convergences and recovers the faster convergence rates.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-05-23T12:04:30.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "fast gradient method",
      "accelerated first order optimisation algorithms",
      "worst-case convergence rate proportional",
      "guarantees iterate convergences",
      "faster convergence rates"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}