Transcription of Alternating Direction Method of Multipliers
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Alternating Direction Method of Multipliers
Alternating Direction Method of MultipliersProf S. BoydEE364b, Stanford Universitysource:Distributed Optimization and Statistical Learning via the AlternatingDirection Method of Multipliers (Boyd, Parikh, Chu, Peleato, Eckstein)1 Goalsrobust methods for arbitrary-scale optimization machine learning/statistics with huge data-sets dynamic optimization on large-scale network decentralized optimization devices/processors/agents coordinate to solve large problem, by passingrelatively small messages2 OutlineDual decompositionMethod of multipliersAlternating Direction Method of multipliersCommon patternsExamplesConsensus and exchangeConclusionsDual decomposition3 Dual problem convex equality constrained optimization problemminimizef(x)subject toAx=b Lagrangian.
dual decomposition (Everett, Dantzig, Wolfe, Benders 1960–65) xk+1 i:= argminx i ... do decomposition Methodofmultipliers 11. Outline Dual decomposition Method of multipliers Alternating direction method of multipliers Common patterns Examples Consensus and …
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