Frick, KlausKlausFrickGrasmair, M.M.Grasmair2018-11-072018-11-072012https://resolver.sub.uni-goettingen.de/purl?gro-2/25217We study the application of the augmented Lagrangian method to the solution of linear ill-posed problems. Previously, linear convergence rates with respect to the Bregman distance have been derived under the classical assumption of a standard source condition. Using the method of variational inequalities, we extend these results in this paper to convergence rates of lower order, both for the case of an a priori parameter choice and an a posteriori choice based on Morozov's discrepancy principle. In addition, our approach allows the derivation of convergence rates with respect to distance measures different from the Bregman distance. As a particular application, we consider sparsity promoting regularization, where we derive a range of convergence rates with respect to the norm under the assumption of restricted injectivity in conjunction with generalized source conditions of Holder type.journal_article10.1088/0266-5611/28/10/104005000310574000006