{
  "id": "1401.0435",
  "version": "v2",
  "published": "2014-01-02T13:44:40.000Z",
  "updated": "2014-05-16T13:49:42.000Z",
  "title": "A global minimization algorithm for Tikhonov functionals with sparsity constraints",
  "authors": [
    "Wei Wang",
    "Stephan W. Anzengruber",
    "Ronny Ramlau",
    "Bo Han"
  ],
  "categories": [
    "math.NA"
  ],
  "abstract": "In this paper we present a globally convergent algorithm for the computation of a minimizer of the Tikhonov functional with sparsity promoting penalty term for nonlinear forward operators in Banach space. The dual TIGRA method uses a gradient descent iteration in the dual space at decreasing values of the regularization parameter $\\alpha_j$, where the approximation obtained with $\\alpha_j$ serves as the starting value for the dual iteration with parameter $\\alpha_{j+1}$. With the discrepancy principle as a global stopping rule the method further yields an automatic parameter choice. We prove convergence of the algorithm under suitable step-size selection and stopping rules and illustrate our theoretic results with numerical experiments for the nonlinear autoconvolution problem.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-05-16T13:49:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65J20",
      "47J06",
      "47A52",
      "49J40"
    ],
    "keywords": [
      "global minimization algorithm",
      "tikhonov functional",
      "sparsity constraints",
      "stopping rule",
      "gradient descent iteration"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1401.0435W"
    }
  }
}