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 MapReduce8211 Numerical

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 Dense Lasso 88 11.2 Distributed 1 Regularized Logistic Regression 92 11.3 Group Lasso with Feature Splitting 95 11.4 Distributed Large-Scale Lasso with MPI 97 11.5 ...

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