DAL solves the dual problem of (1) via the augmented Lagrangian method (see Bertsekas 82). It uses the analytic expression (and its derivatives) of the following soft-thresholding operation， which can be computed for L1 and grouped L1 (and many other) sparsity inducing regularizers. If you are interested in our algorithm please find more details in our technical report or in my talk at Optimization for Machine Learning Workshop (NIPS 2009).

75448149dal_ver1.01.tar

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