{
  "id": "1412.0126",
  "version": "v1",
  "published": "2014-11-29T16:52:38.000Z",
  "updated": "2014-11-29T16:52:38.000Z",
  "title": "A Generalization of the Chambolle-Pock Algorithm to Banach Spaces with Applications to Inverse Problems",
  "authors": [
    "Thorsten Hohage",
    "Carolin Homann"
  ],
  "categories": [
    "math.OC"
  ],
  "abstract": "For a Hilbert space setting Chambolle and Pock introduced an attractive first-order algorithm which solves a convex optimization problem and its Fenchel dual simultaneously. We present a generalization of this algorithm to Banach spaces. Moreover, under certain conditions we prove strong convergence as well as convergence rates. Due to the generalization the method becomes efficiently applicable for a wider class of problems. This fact makes it particularly interesting for solving ill-posed inverse problems on Banach spaces by Tikhonov regularization or the iteratively regularized Newton-type method, respectively.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-11-29T16:52:38.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "banach spaces",
      "chambolle-pock algorithm",
      "generalization",
      "applications",
      "hilbert space setting chambolle"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1412.0126H"
    }
  }
}