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

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.