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This technical note is an ancillary material for our research paper (Itoh andParente, 2019). We discuss an alternating direction method of multipliers withgeneralized augmented terms (ADMM-GAT) and introduce a generalized residualbalance technique for efficiently employing ADMM-GAT. These techniques areapplied to least absolute deviation and its constrained version and theiralgorithmic details are presented. These algorithms are used for theimplementation of the method described in (Itoh and Parente, 2019).

A note on alternating direction method of multipliers with generalized augmented terms for constrained sparse least absolute deviation