method of multipliers [@Bertsekas97-ParallelDistributed]. For the inner loop, common choices are the nonlinear Gauss-Seidel method [@Spars09; @Jakovetic11-CooperativeConvexOptimization] and Jacobi type algorithms, such as the diagonal quadratic approximation [@Ruszczynski]. In [@Mota11ICASSP] we applied fast gradient algorithms [@BeckTeboulleFISTA] in both loops. We mention that, although [@Ruszczynski; @Spars09; @Mota11ICASSP] do not address  specifically, they can be easily adapted to solve it, as explained in section \[Sec:RelatedAlgs\].

A special augmented Lagrangian-based algorithm, which uses one loop only, is the alternating direction method of multipliers (ADMM) [@Glowinski75-ADMMFirst; @Gabay76-ADMMFirst; @Bertsekas97-ParallelDistributed]. In fact, ADMM is the method of multipliers concatenated with one iteration of the nonlinear Gauss-Seidel, and therefore, it consists of just one loop. ADMM is not directly applicable to : one has to reformulate that problem first. There are several options for such reformulation. For example, [@Zhu09-DistributedInNetworkChannelCoding] proposes a distributed algorithm for solving specific instance of , based on a particular reformulation (the works [@Bazerque10-DistributedSpectrumSensing; @Kim11-CooperativeSpectrumSensingKrigedKalmanFiltering; @Forero10-ConsensusBasedDistributedSVMs; @Erseghe11-FastConsensusByADMM] apply the same algorithm to other instances of ). Another possible reformulation of  is explored in [@Schizas08-ConsensusAdHocWSNsPartI; @Schizas08-ConsensusAdHocWSNsPartII], which also proposes an ADMM-based algorithm, but in contrast with [@Zhu09-DistributedInNetworkChannelCoding], it uses two communication steps per iteration, or in other words, each node uses information from its second-order 