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Inexact Search Directions in Interior Point Methods for Large Scale Optimization
Published on Jan 15, 20135273 Views
Interior Point Methods (IPMs) for linear and quadratic optimization have been very successful but occasionally they struggle with excessive memory requirements and high computational costs per iterati
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Chapter list
Inexact Search Directions in Interior Point Methods for Large Scale Optimization00:00
Outline00:53
1st-order Methods for Optimization02:07
Interior Point Methods (IPMs)03:17
Observation03:42
Just think04:45
Interior Point Methods05:18
LO & QO Problems05:22
Interior-Point Framework06:31
The First Order Optimality Conditions07:26
Central Path08:47
Path Following Method09:27
Standard complexity result10:02
Standard IPMs for LO/QO10:35
Objective: Accelerate IPMs for LO/QO11:10
Exact Newton Method11:49
General Assumption12:06
Short-step (Feasible) Algorithm12:36
Theorem13:11
Proof (key ideas)14:30
Conclusion15:08
Observation15:38
From Theory to Practice16:11
Sparse Approximations16:26
Bayesian Statistics Viewpoint17:00
Wavelet-based Signal/Image Reconstruction17:12
Compressed Sensing17:34
LO/QO Reformulations18:12
Two-way Orthogonality of A19:17
Restricted Isometry Property20:33
Problem Reformulation21:35
Preconditioner23:16
Spectral Properties of P−1M23:52
Preconditioning25:03
Computational Results: Comparing MatVecs26:16
Ranking of nodes in networks27:09
Google Problem (1)27:54
Google Problem (2)29:18
Preconditioner for Google Problem29:52
Computational Results: mf-IPM30:33
New IPMs31:38
Thank You!33:42