{
  "id": "1307.4302",
  "version": "v1",
  "published": "2013-07-15T13:59:30.000Z",
  "updated": "2013-07-15T13:59:30.000Z",
  "title": "Lipschitz gradients for global optimization in a one-point-based partitioning scheme",
  "authors": [
    "Dmitri E. Kvasov",
    "Yaroslav D. Sergeyev"
  ],
  "comment": "25 pages, 4 figures, 5 tables. arXiv admin note: text overlap with arXiv:1103.2056",
  "journal": "Journal of Computational and Applied Mathematics Volume 236, Issue 16, October 2012, Pages 4042-4054",
  "doi": "10.1016/j.cam.2012.02.020",
  "categories": [
    "math.OC",
    "cs.MS",
    "cs.NA",
    "math.NA"
  ],
  "abstract": "A global optimization problem is studied where the objective function $f(x)$ is a multidimensional black-box function and its gradient $f'(x)$ satisfies the Lipschitz condition over a hyperinterval with an unknown Lipschitz constant $K$. Different methods for solving this problem by using an a priori given estimate of $K$, its adaptive estimates, and adaptive estimates of local Lipschitz constants are known in the literature. Recently, the authors have proposed a one-dimensional algorithm working with multiple estimates of the Lipschitz constant for $f'(x)$ (the existence of such an algorithm was a challenge for 15 years). In this paper, a new multidimensional geometric method evolving the ideas of this one-dimensional scheme and using an efficient one-point-based partitioning strategy is proposed. Numerical experiments executed on 800 multidimensional test functions demonstrate quite a promising performance in comparison with popular DIRECT-based methods.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-07-15T13:59:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65K05",
      "90C26",
      "90C56"
    ],
    "keywords": [
      "global optimization",
      "one-point-based partitioning scheme",
      "lipschitz gradients",
      "multidimensional test functions demonstrate quite",
      "multidimensional black-box function"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1307.4302K"
    }
  }
}