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 Regular

8 Distributed Model Fitting 61 8.1 Examples 62 8.2 Splitting across Examples 64 8.3 Splitting across Features 66 9 Nonconvex Problems 73 9.1 Nonconvex Constraints 73 9.2 Bi-convex Problems 76 10 Implementation 78 10.1 Abstract Implementation 78 10.2 MPI 80 10.3 Graph Computing Frameworks 81 10.4 MapReduce 82 11 Numerical Examples 87 11.1 Small ...

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