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Convergence Rates of Inexact Proximal-Gradient Methods for Convex Optimization
Published on Jan 25, 20126926 Views
We consider the problem of optimizing the sum of a smooth convex function and a non-smooth convex function using proximal-gradient methods, where an error is present in the calculation of the gradient
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Convergence Rates of Inexact Proximal-Gradient Methods for Convex Optimization00:00
Outline - 100:00
Composite Convex Optimization Problems - 100:15
Composite Convex Optimization Problems - 200:30
Fast Convergence Rates of Proximal-Gradient Methods - 100:52
Fast Convergence Rates of Proximal-Gradient Methods - 200:56
Fast Convergence Rates of Proximal-Gradient Methods - 301:13
Fast Convergence Rates of Proximal-Gradient Methods - 401:29
Fast Convergence Rates of Proximal-Gradient Methods - 501:35
Overview of the Basic Gradient Method - 101:47
Overview of the Basic Gradient Method - 201:54
Overview of the Basic Gradient Method - 302:13
Overview of the Basic Gradient Method - 402:22
Overview of the Basic Proximal-Gradient Method - 102:31
Overview of the Basic Proximal-Gradient Method - 202:36
Overview of the Basic Proximal-Gradient Method - 302:42
Overview of the Basic Proximal-Gradient Method - 402:47
Overview of the Basic Proximal-Gradient Method - 502:53
Special case of Projected-Gradient Methods - 103:02
Special case of Projected-Gradient Methods - 203:15
Special case of Projected-Gradient Methods - 303:27
Special case of Projected-Gradient Methods - 403:36
Special case of Projected-Gradient Methods - 503:44
Special case of Iterative Soft-Thresholding Methods - 104:17
Special case of Iterative Soft-Thresholding Methods - 204:27
Special case of Iterative Soft-Thresholding Methods - 304:36
Special case of Iterative Soft-Thresholding Methods - 404:39
Special case of Iterative Soft-Thresholding Methods - 504:42
Special case of Iterative Soft-Thresholding Methods - 605:05
Accelerated (Proximal-) Gradient Methods - 105:26
Accelerated (Proximal-) Gradient Methods - 205:35
Accelerated (Proximal-) Gradient Methods - 305:49
Exact Proximal-Gradient Methods - 105:55
Exact Proximal-Gradient Methods - 206:03
Exact Proximal-Gradient Methods - 306:14
Inexact Proximal-Gradient Methods - 106:24
Inexact Proximal-Gradient Methods - 206:26
Summary of Contribution - 106:47
Summary of Contribution - 206:58
Summary of Contribution - 307:05
Summary of Contribution - 407:12
Outline - 207:22
Prior Work: Stochastic Proximal-Gradient Methods - 107:28
Prior Work: Stochastic Proximal-Gradient Methods - 207:37
Prior Work: Stochastic Proximal-Gradient Methods - 307:43
Prior Work: Projected-Gradient Methods (Fixed Error) - 107:58
Prior Work: Projected-Gradient Methods (Fixed Error) - 208:03
Prior Work: Projected-Gradient Methods (Fixed Error) - 308:08
Prior Work: Projected-Gradient Methods (Variable Error) - 108:19
Prior Work: Projected-Gradient Methods (Variable Error) - 208:22
Prior Work: Projected-Gradient Methods (Variable Error) - 308:29
Prior Work: Proximal-Gradient Methods - 108:42
Prior Work: Proximal-Gradient Methods - 208:45
Prior Work: Proximal-Gradient Methods - 308:55
Outline - 309:01
Problem Setting and Algorithm - 109:06
Problem Setting and Algorithm - 209:15
Central Assumptions and Notation - 109:20
Central Assumptions and Notation - 209:41
Central Assumptions and Notation - 309:58
Central Assumptions and Notation - 410:06
Fast Convergence Rates of Proximal-Gradient Methods - 110:26
Fast Convergence Rates of Proximal-Gradient Methods - 210:36
Convexity - Basic Proximal-Gradient Method - 110:43
Convexity - Basic Proximal-Gradient Method - 210:55
Convexity - Basic Proximal-Gradient Method - 311:02
Convexity - Accelerated Proximal-Gradient Method - 111:12
Convexity - Accelerated Proximal-Gradient Method - 211:26
Convexity - Accelerated Proximal-Gradient Method - 311:29
Strongly Convex Objectives - 111:44
Strongly Convex Objectives - 211:48
Strongly Convex Objectives - 312:03
Strong Convexity - Basic Proximal-Gradient Method - 112:07
Strong Convexity - Basic Proximal-Gradient Method - 212:22
Strong Convexity - Accelerated Method - 112:34
Strong Convexity - Accelerated Method - 212:47
Outline - 412:56
CUR-like factorization with the l2-norm - 113:01
CUR-like factorization with the l2-norm - 213:17
CUR-like factorization with the l2-norm - 313:39
Comparison against a xed prox solution accuracy13:56
Comparison against a xed number of prox iterations14:23
Comparison of di erent prox accuracy decays14:33
Discussion - 114:52
Discussion - 215:14
Discussion - 315:24
Summary - 115:44
Summary - 215:51
Summary - 315:54
Summary - 415:59