{
  "id": "1902.04794",
  "version": "v1",
  "published": "2019-02-13T09:00:19.000Z",
  "updated": "2019-02-13T09:00:19.000Z",
  "title": "Analysis of the Block Coordinate Descent Method for Non-linear Ill-Posed Problems",
  "authors": [
    "Simon Rabanser",
    "Lukas Neumann",
    "Markus Haltmeier"
  ],
  "categories": [
    "math.NA"
  ],
  "abstract": "Block coordinate descent (BCD) methods approach optimization problems by performing gradient steps along alternating subgroups of coordinates. This is in contrast to full gradient descent, where a gradient step updates all coordinates simultaneously. BCD has been demonstrated to accelerate the gradient method in many practical large-scale applications. Despite its success no convergence analysis for inverse problems is known so far. In this paper, we investigate the BCD method for solving linear and non-linear ill-posed inverse problems. As main theoretical result, we show that for operators having a particular tensor product form, the BCD method combined with an appropriate stopping criterion yields a convergent regularization method. To illustrate the theory, we perform numerical experiments comparing the BCD and the full gradient descent method for the non-linear inverse problem of one-step inversion in multi-spectral X-ray tomography.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-02-13T09:00:19.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "block coordinate descent method",
      "non-linear ill-posed problems",
      "inverse problem",
      "bcd method",
      "gradient step"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}