{
  "id": "1603.07490",
  "version": "v1",
  "published": "2016-03-24T09:19:56.000Z",
  "updated": "2016-03-24T09:19:56.000Z",
  "title": "Landweber-Kaczmarz method in Banach spaces with inexact inner solvers",
  "authors": [
    "Qinian Jin"
  ],
  "comment": "To appear in Inverse Problems",
  "categories": [
    "math.NA"
  ],
  "abstract": "In recent years Landweber(-Kaczmarz) method has been proposed for solving nonlinear ill-posed inverse problems in Banach spaces using general convex penalty functions. The implementation of this method involves solving a (nonsmooth) convex minimization problem at each iteration step and the existing theory requires its exact resolution which in general is impossible in practical applications. In this paper we propose a version of Landweber-Kaczmarz method in Banach spaces in which the minimization problem involved in each iteration step is solved inexactly. Based on the $\\varepsilon$-subdifferential calculus we give a convergence analysis of our method. Furthermore, using Nesterov's strategy, we propose a possible accelerated version of Landweber-Kaczmarz method. Numerical results on computed tomography and parameter identification in partial differential equations are provided to support our theoretical results and to demonstrate our accelerated method.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-03-24T09:19:56.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "banach spaces",
      "inexact inner solvers",
      "landweber-kaczmarz method",
      "general convex penalty functions",
      "iteration step"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}