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Non Smooth, Non Finite, and Non Convex Optimization
Published on Sep 13, 20157544 Views
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Chapter list
Non-Smooth, Non-Finite, and Non-Convex Optimization 00:00
Complex-Step Derivative - 100:29
Complex-Step Derivative - 201:28
Complex-Step Derivative - 302:10
“Subgradients” of Non-Convex functions - 102:44
“Subgradients” of Non-Convex functions - 203:16
“Subgradients” of Non-Convex functions - 303:51
Stochastic Variance-Reduced Gradient - 104:29
Stochastic Variance-Reduced Gradient - 205:23
Stochastic Variance-Reduced Gradient - 306:00
Review of Part 1 and Motivation for Part 206:36
Outline - 108:54
Motivation: Sparse Regularization - 1 09:01
Motivation: Sparse Regularization - 209:11
Motivation: Sparse Regularization - 309:27
Motivation: Sparse Regularization - 409:39
Smoothing Approximations of Non-Smooth Functions - 110:00
Smoothing Approximations of Non-Smooth Functions - 210:11
Smoothing Approximations of Non-Smooth Functions - 310:18
Smoothing Approximations of Non-Smooth Functions - 410:36
Smoothing Approximations of Non-Smooth Functions - 511:47
Discussion of Smoothing Approach - 112:11
Discussion of Smoothing Approach - 213:35
Discussion of Smoothing Approach - 314:27
Converting to Constrained Optimization - 114:39
Converting to Constrained Optimization - 214:51
Converting to Constrained Optimization - 315:07
Converting to Constrained Optimization - 415:16
Converting to Constrained Optimization - 515:21
Optimization with Simple Constraints - 115:34
Optimization with Simple Constraints - 215:51
Optimization with Simple Constraints - 316:09
Gradient Projection - 116:23
Gradient Projection - 216:29
Gradient Projection - 316:35
Gradient Projection - 416:43
Gradient Projection - 516:49
Discussion of Projected Gradient - 117:57
Discussion of Projected Gradient - 218:13
Discussion of Projected Gradient - 318:33
Projection Onto Simple Sets - 119:09
Projection Onto Simple Sets - 221:01
Proximal-Gradient Method - 121:24
Proximal-Gradient Method - 221:57
Proximal-Gradient Method - 322:37
Proximal Operator, Iterative Soft Thresholding - 123:49
Proximal Operator, Iterative Soft Thresholding - 223:53
Proximal Operator, Iterative Soft Thresholding - 324:08
Proximal Operator, Iterative Soft Thresholding - 424:14
Proximal Operator, Iterative Soft Thresholding - 524:23
Exact Proximal-Gradient Methods - 124:50
Exact Proximal-Gradient Methods - 224:53
Exact Proximal-Gradient Methods - 324:58
Exact Proximal-Gradient Methods - 425:11
Exact Proximal-Gradient Methods - 525:16
Alternating Direction Method of Multipliers - 127:30
Alternating Direction Method of Multipliers - 227:56
Alternating Direction Method of Multipliers - 328:29
Alternating Direction Method of Multipliers - 428:32
Frank-Wolfie Method - 128:51
Frank-Wolfie Method - 229:10
Summary - 130:13
Outline - 235:02
Stochastic vs. Deterministic for Stochastic Objectives - 135:13
Stochastic vs. Deterministic for Stochastic Objectives - 236:15
Stochastic vs. Deterministic for Stochastic Objectives - 337:10
Stochastic vs. Deterministic for Stochastic Objectives - 439:17
Stochastic vs. Deterministic for Stochastic Objectives - 540:25
Stochastic vs. Deterministic for Stochastic Objectives - 640:56
Stochastic vs. Deterministic for Stochastic Objectives - 741:28
Stochastic vs. Deterministic for Stochastic Objectives - 842:15
Stochastic vs. Deterministic for Stochastic Objectives - 943:46
Streaming SVRG - 144:56
Streaming SVRG - 245:12
Streaming SVRG - 345:17
Streaming SVRG - 457:12
Constant-Step SG under Strong Assumptions - 159:53
Constant-Step SG under Strong Assumptions - 201:01:13
Constant-Step SG under Strong Assumptions - 301:04:44
Online Convex Optimization - 101:05:58
Online Convex Optimization - 201:06:06
Online Convex Optimization - 301:06:07
Online Convex Optimization - 401:06:16
Online Convex Optimization - 501:06:16
Outline - 301:06:35
Two Classic Perspectives of Non-Convex Optimization - 101:06:44
Two Classic Perspectives of Non-Convex Optimization - 201:06:46
Two Classic Perspectives of Non-Convex Optimization - 301:07:17
Two Classic Perspectives of Non-Convex Optimization - 401:07:29
Two Classic Perspectives of Non-Convex Optimization - 501:07:53
Strong Property: Expanding the Second Phase - 101:09:14
Strong Property: Expanding the Second Phase - 201:09:23
Strong Property: Expanding the Second Phase - 301:09:41
Strong Property: Expanding the Second Phase - 401:13:17
Global Linear Convergence with the Strong Property - 101:13:23
Global Linear Convergence with the Strong Property - 201:13:27
General Global Non-Convex Rates? - 101:14:42
General Global Non-Convex Rates? - 201:15:35
Escaping Saddle Points - 101:17:18
Escaping Saddle Points - 201:17:37
Escaping Saddle Points - 301:19:49
Globally-Optimal Methods for Matrix Problems - 101:19:52
Globally-Optimal Methods for Matrix Problems - 201:25:58
Globally-Optimal Methods for Matrix Problems - 301:26:21
Globally-Optimal Methods for Matrix Problems - 401:28:31
Globally-Optimal Methods for Matrix Problems - 501:28:58
Convex Relaxation/Representations - 101:30:54
Convex Relaxation/Representations - 201:31:23
Convex Relaxation/Representations - 301:31:40
General Non-Convex Rates - 101:31:47
General Non-Convex Rates - 201:31:49
General Non-Convex Rates - 301:31:50
Summary - 301:32:05