{
  "id": "2211.08578",
  "version": "v1",
  "published": "2022-11-15T23:49:25.000Z",
  "updated": "2022-11-15T23:49:25.000Z",
  "title": "Anderson acceleration of gradient methods with energy for optimization problems",
  "authors": [
    "Hailiang Liu",
    "Jia-Hao He",
    "Xuping Tian"
  ],
  "comment": "18 pages, 4 figures",
  "categories": [
    "math.OC"
  ],
  "abstract": "Anderson acceleration (AA) as an efficient technique for speeding up the convergence of fixed-point iterations may be designed for accelerating an optimization method. We propose a novel optimization algorithm by adapting Anderson acceleration to the energy adaptive gradient method (AEGD) [arXiv:2010.05109]. The feasibility of our algorithm is examined in light of convergence results for AEGD, though it is not a fixed-point iteration. We also quantify the accelerated convergence rate of AA for gradient descent by a factor of the gain at each implementation of the Anderson mixing. Our experimental results show that the proposed algorithm requires little tuning of hyperparameters and exhibits superior fast convergence.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-11-15T23:49:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65K10",
      "68Q25"
    ],
    "keywords": [
      "optimization problems",
      "fixed-point iteration",
      "energy adaptive gradient method",
      "novel optimization algorithm",
      "superior fast convergence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}