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On a heuristic stopping rule for the regularization of inverse problems by the augmented Lagrangian method

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Abstract

In this paper we propose a heuristic stopping rule of Hanke–Raus type for the regularization of linear ill-posed inverse problems by the augmented Lagrangian method. This stopping rule requires no information on the noise level. Under certain source conditions, we derive a posteriori error estimates in term of Bregman distance. By imposing certain conditions on the noise data, we establish convergence results. Numerical results are presented to illustrate the performance.

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Authors and Affiliations

  1. Mathematical Sciences Institute, Australian National University, Canberra, ACT, 2601, Australia

    Qinian Jin

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  1. Qinian Jin
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Correspondence to Qinian Jin.

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Jin, Q. On a heuristic stopping rule for the regularization of inverse problems by the augmented Lagrangian method. Numer. Math. 136, 973–992 (2017). https://doi.org/10.1007/s00211-016-0860-8

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  • DOI: https://doi.org/10.1007/s00211-016-0860-8

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