Convex optimization algorithms:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Belmont, Massachusetts
Athena Scientific
[2015]
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xii, 564 Seiten Illustrationen, Diagramme |
| ISBN: | 9781886529281 1886529280 |
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MARC
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| adam_text |
Titel: Convex optimization algorithms
Autor: Bertsekas, Dimitri P
Jahr: 2015
Contents
Convex Optimization Models: An Overview
1.1. Lagrange Duality.
1.1.1. Separable Problems - Decomposition
1.1.2. Partitioning.
1.2. Fenchel Duality and Conic Programming .
1.2.1. Linear Conic Problems .
1.2.2. Second Order Cone Programming . .
1.2.3. Semidefinite Programming . .
1.3. Additive Cost Problems.
1.4. Large Number of Constraints . . .
1.5. Exact Penalty Functions .
1.6. Notes, Sources, and Exercises . .
p. 2
p. 7
p. 9
p. 10
p. 15
p. 17
p. 22
p. 25
p. 34
p. 39
p. 47
2. Optimization Algorithms: An Overview.p. 53
2.1. Iterative Descent Algorithms.p. 55
2.1.1. Differentiable Cost Function Descent - Unconstrained .
Problems .p. 58
2.1.2. Constrained Problems - Feasible Direction Methods . . . p. 71
2.1.3. Nondifferentiable Problems - Subgradient Methods . . . p. 78
2.1.4. Alternative Descent Methods.p. 80
2.1.5. Incremental Algorithms.p. 83
2.1.6. Distributed Asynchronous Iterative Algorithms . p. 104
2.2. Approximation Methods .p. 106
2.2.1. Polyhedral Approximation.p. 107
2.2.2. Penalty, Augmented Lagrangian, and Inferior .
Point Methods.p. 108
2.2.3. Proximal Algorithm, Bündle Methods, and.
Tikhonov Regularization.p. 110
2.2.4. Alternating Direction Method of Multipliers.p. 111
2.2.5. Smoothing of Nondifferentiable Problems .p. 113
2.3. Notes, Sources, and Exercises .p. 119
3. Subgradient Methods.p. 135
3.1. Subgradients of Convex Real-Valued Functions.p. 136
iv Contents
3.1.1. Characterization of the Subdifferential. p. 146
3.2. Convergence Analysis of Subgradient Methods. p. 148
3.3. e-Subgradient Methods . p. 162
3.3.1. Connection with Incremental Subgradient Methods . . p. 166
3.4. Notes, Sources, and Exercises. p. 167
4. Polyhedral Approximation Methods. p. 181
4.1. Outer Linearization - Cutting Plane Methods . p. 182
4.2. Inner Linearization - Simplicial Decomposition. p. 188
4.3. Duality of Outer and Inner Linearization. p. 194
4.4. Generalized Polyhedral Approximation. p. 196
4.5. Generalized Simplicial Decomposition. p. 209
4.5.1. Differentiable Cost Case. p. 213
4.5.2. Nondifferentiable Cost and Side Constraints. p. 213
4.6. Polyhedral Approximation for Conic Programming . p. 217
4.7. Notes, Sources, and Exercises. p. 228
5. Proximal Algorithms . p. 233
5.1. Basic Theory of Proximal Algorithms. p. 234
5.1.1. Convergence. p. 235
5.1.2. Rate of Convergence. p. 239
5.1.3. Gradient Interpretation. p. 246
5.1.4. Fixed Point Interpretation, Overrelaxation,.
and Generalization. p. 248
5.2. Dual Proximal Algorithms. p. 256
5.2.1. Augmented Lagrangian Methods. p. 259
5.3. Proximal Algorithms with Linearization. p. 268
5.3.1. Proximal Cutting Plane Methods. p. 270
5.3.2. Bündle Methods. p. 272
5.3.3. Proximal Inner Linearization Methods. p. 276
5.4. Alternating Direction Methods of Multipliers. p. 280
5.4.1. Applications in Machine Learning. p. 286
5.4.2. ADMM Applied to Separable Problems. p. 289
5.5. Notes, Sources, and Exercises. p. 293
6. Additional Algorithmic Topics. p. 301
6.1. Gradient Projection Methods. p. 302
6.2. Gradient Projection with Extrapolation. p. 322
6.2.1. An Algorithm with Optimal Iteration Complexity . . . p. 323
6.2.2. Nondifferentiable Cost - Smoothing. p. 326
6.3. Proximal Gradient Methods. p. 330
6.4. Incremental Subgradient Proximal Methods. p. 340
6.4.1. Convergence for Methods with Cyclic Order. p. 344
Contents v
6.4.2. Convergence for Methods with Randomized Order . . p. 353
6.4.3. Application in Specially Structured Problems. p. 361
6.4.4. Incremental Constraint Projection Methods. p. 365
6.5. Coordinate Descent Methods. p. 369
6.5.1. Variants of Coordinate Descent. p. 373
6.5.2. Distributed Asynchronous Coordinate Descent . p. 376
6.6. Generalized Proximal Methods. p. 382
6.7. e-Descent and Extended Monotropic Programming . p. 396
6.7.1. e-Subgradients. p. 397
6.7.2. e-Descent Method. p. 400
6.7.3. Extended Monotropic Programming Duality. p. 406
6.7.4. Special Cases of Strong Duality. p. 408
6.8. Inferior Point Methods . p. 412
6.8.1. Primal-Dual Methods for Linear Programming . p. 416
6.8.2. Inferior Point Methods for Conic Programming . p. 423
6.8.3. Central Cutting Plane Methods. p. 425
6.9. Notes, Sources, and Exercises. p. 426
Appendix A: Mathematical Background. p. 443
A.l. Linear Algebra. p. 445
A.2. Topological Properties . p. 450
A.3. Derivatives . p. 456
A.4. Convergence Theorems. p. 458
Appendix B: Convex Optimization Theory: A Summary . p. 467
B.l. Basic Concepts of Convex Analysis. p. 467
B.2. Basic Concepts of Polyhedral Convexity. p. 489
B.3. Basic Concepts of Convex Optimization. p. 494
B.4. Geometrie Duality Framework. p. 498
B.5. Duality and Optimization. p. 505
References.p. 519
Index.p. 557 |
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| author | Bertsekas, Dimitri P. 1942- |
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| author_facet | Bertsekas, Dimitri P. 1942- |
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| bvnumber | BV042442048 |
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| ctrlnum | (OCoLC)908339429 (DE-599)OBVAC12182784 |
| discipline | Mathematik |
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| id | DE-604.BV042442048 |
| illustrated | Illustrated |
| indexdate | 2024-11-29T09:00:30Z |
| institution | BVB |
| isbn | 9781886529281 1886529280 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027877323 |
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| owner_facet | DE-20 DE-83 DE-29T DE-706 DE-703 |
| physical | xii, 564 Seiten Illustrationen, Diagramme |
| publishDate | 2015 |
| publishDateSearch | 2015 |
| publishDateSort | 2015 |
| publisher | Athena Scientific |
| record_format | marc |
| spelling | Bertsekas, Dimitri P. 1942- Verfasser (DE-588)171165519 aut Convex optimization algorithms Dimitri P. Bertsekas (Massachusetts Institute of Technology) Belmont, Massachusetts Athena Scientific [2015] xii, 564 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Konvexe Optimierung (DE-588)4137027-2 gnd rswk-swf Konvexe Optimierung (DE-588)4137027-2 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027877323&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bertsekas, Dimitri P. 1942- Convex optimization algorithms Konvexe Optimierung (DE-588)4137027-2 gnd |
| subject_GND | (DE-588)4137027-2 |
| title | Convex optimization algorithms |
| title_auth | Convex optimization algorithms |
| title_exact_search | Convex optimization algorithms |
| title_full | Convex optimization algorithms Dimitri P. Bertsekas (Massachusetts Institute of Technology) |
| title_fullStr | Convex optimization algorithms Dimitri P. Bertsekas (Massachusetts Institute of Technology) |
| title_full_unstemmed | Convex optimization algorithms Dimitri P. Bertsekas (Massachusetts Institute of Technology) |
| title_short | Convex optimization algorithms |
| title_sort | convex optimization algorithms |
| topic | Konvexe Optimierung (DE-588)4137027-2 gnd |
| topic_facet | Konvexe Optimierung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027877323&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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