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Primal-Dual Subgradient Methods for Huge-Scale Problems
Published on Aug 26, 20135891 Views
We consider a new class of huge-scale problems, the problems with sparse subgradients. The most important functions of this type are piece-wise linear. For optimization problems with uniform sparsity
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Chapter list
Primal-dual subgradient methods for huge-scale problems00:00
Outline00:07
Nonlinear Optimization: problems sizes00:35
Sparse problems04:38
Example: Gradient Method06:53
Sparse updating strategy08:17
When it can work?12:01
Fast updates in short computational trees16:58
Main advantages17:27
Simple subgradient methods17:59
Constrained minimization (N.Shor (1964) & B.Polyak)20:45
Linear Conic Problems25:40
Functional constraints29:49
Examples37:03
New Dual Problem38:01
Primal and dual minimization sequences45:28
Convergence45:34
Example: Solving huge LP47:02
Computational experiments: Iteration Cost48:27
Convergence of GMs : Large Scale Yu.51:04
Thank you for your attention!52:55