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Foundations and TrendsR inMachine LearningVol. 3, No. 1 (2010) 1 122c 2011 S. Boyd, N. Parikh, E. Chu, B. Peleatoand J. EcksteinDOI: Optimization and StatisticalLearning via the Alternating DirectionMethod of MultipliersStephen Boyd1, Neal Parikh2, Eric Chu3Borja Peleato4and Jonathan Eckstein51Electrical Engineering Department, Stanford University, Stanford, CA94305, USA, Science Department, Stanford University, Stanford, CA 94305,USA, Engineering Department, Stanford University, Stanford, CA94305, USA, Engineering Department, Stanford University, Stanford, CA94305, USA, Science and Information Systems Department andRUTCOR, Rutgers University, Piscataway, NJ 08854, Introduction32 Dual Dual Augmented Lagrangians and the Method of Multipliers103 Alternating Direction Method of Optimality Conditions and Stopping Extensions and Notes and References234 General Proximity Quadratic Objective Smooth Objective Decomposition315 Constrained Convex Convex Linear and Quadratic Programming366 1-Norm Least Absolute Basis General 1Regularized Loss Sparse Inverse Covariance Selection457 Consensus and Global Variable Consensus General Form Consensus Sharing568 Distribut

Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers Stephen Boyd1, ... 4.2 Quadratic Objective Terms 26 4.3 Smooth Objective Terms 30 4.4 Decomposition 31 ... cable in many other cases, such as in engineering design, multi-period

  Multi, Objectives, Optimization