Distributed Optimization and Statistical Learning via the ...

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 Chu3 Borja Peleato4and Jonathan Eckstein51 Electrical 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 1 Regularized Loss Sparse Inverse Covariance Selection457 Consensus and Global Variable Consensus General Form Consensus Sharing568 Distributed Model Splitting across Splitting across Features669 Nonconvex Nonconvex Bi-convex Problems7610 Abstract Graph Computing

to look to parallel optimization algorithms as a mechanism for solving large-scale statistical tasks. This approach also has the benefit that one algorithm could be flexible enough to solve many problems. This review discusses the alternating direction method of multipli-ers (ADMM), a simple but powerful algorithm that is well suited to

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  Solving, Distributed, Optimization, Distributed optimization

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