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Alternating Direction Method of Multipliers
Published on Jan 25, 201250839 Views
Problems in areas such as machine learning and dynamic optimization on a large network lead to extremely large convex optimization problems, with problem data stored in a decentralized way, and proces
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Chapter list
Alternating Direction Method of Multipliers00:00
Goals01:20
Outline - 0104:07
Dual problem04:28
Dual ascent05:55
Dual decomposition - 0107:29
Dual decomposition - 0208:17
Outline - 0209:07
Method of multipliers - 0109:17
Method of multipliers dual update step10:46
Method of multipliers - 0211:58
Outline - 0313:33
Alternating direction method of multipliers - 0113:35
Alternating direction method of multipliers - 0214:17
Alternating direction method of multipliers - 0315:46
ADMM and optimality conditions16:07
Convergence18:17
Related algorithms21:45
ADMM with scaled dual variables23:22
Common patterns 23:58
Decomposition27:05
Proximal operator27:41
Quadratic objective29:40
Smooth objective32:17
Outline - 0433:39
Constrained convex optimization33:41
Lasso35:55
Lasso example37:17
Sparse inverse covariance selection38:43
Sparse inverse covariance selection via ADMM39:50
Analytical solution for X-update40:54
Sparse inverse covariance selection example41:09
Outline - 0541:39
Consensus optimization41:52
Consensus optimization via ADMM - 0143:24
Consensus optimization via ADMM - 0244:03
Statistical interpretation45:33
Consensus classification46:57
Consensus SVM example47:40
Iteration 148:29
Iteration 549:01
Iteration 4049:07
Distributed lasso example50:04
Exchange problem53:21
Exchange ADMM54:48
Interpretation as tatonnement process55:45
Distributed dynamic energy management55:49
Summary and conclusions56:22