Problem complexity and method efficiency in optimization:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Chichester u.a.
Wiley
1983
|
| Series: | Wiley-Interscience series in discrete mathematics
A Wiley-Interscience publication |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Aus dem Russ. übers. |
| Physical Description: | XV, 388 S. |
| ISBN: | 0471103454 |
Staff View
MARC
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| 245 | 1 | 0 | |a Problem complexity and method efficiency in optimization |c A. S. Nemirovsky ; D. B. Yudin |
| 264 | 1 | |a Chichester u.a. |b Wiley |c 1983 | |
| 300 | |a XV, 388 S. | ||
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Record in the Search Index
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|---|---|
| adam_text | Contents
1 INTRODUCTION i
1.1 Formulation of the problem of estimating the complexity
of optimization problems, and the main results of the
work. An informal description 1
1.2 Families of mathematical programming problems.
Approximate solutions and their error 10
1.3 Numerical methods of solving mathematical program¬
ming problems 16
1.4 Characteristics of methods on a problem and on a class.
Complexity 23
1.5 Some propositions about mathematical programming
methods 29
1.6 On the complexity of classes of multi extremal problems 35
1.7 Proof of Theorem 1.3.4 38
2 CONVEX PROGRAMMING.
LINEARLY CONVERGENT METHODS
FOR CLASSES OF GENERAL CONVEX
PROBLEMS 42
2.1 Convex sets and convex problems 42
2.2 Classes of convex extremal problems 50
2.3 The centres of gravity method for solving general convex
problems 57
2.4 Special versions of the MCG 65
2.5 A realizable version of the MCG 72
v
vi Contents
3 METHODS OF MIRROR DESCENT 83
3.1 The idea of the methods 83
3.2 Regular spaces 89
3.3 MD methods on classes of Lipschitz convex problems 93
3.4 MD methods on classes of general convex problems 107
3.5 Some additional proofs 120
4 COMPLEXITY OF CLASSES OF
GENERAL CONVEX PROBLEMS
(EXACT FIRST ORDER ORACLE) 125
4.1 Complexity of classes of general convex problems 125
4.2 Complexity of classes of Lipschitz convex problems 137
4.3 Recommendations about the use of methods of solving
general convex or Lipschitz convex problems 142
4.4 Proof of lower bounds for the complexity. I 151
4.5 Proof of lower bounds for the complexity. II 164
4.6 Proof of lower bounds for the complexity. Ill 174
5 PROBLEMS OF CONVEX
STOCHASTIC PROGRAMMING isi
5.1 Classes of convex stochastic programming problems 182
5.2 Unconstrained optimization 188
5.3 The complexity of stochastic programming problems 197
6 SOLUTION OF CONVEX CONCAVE
GAMES AND CONSTRAINED
STOCHASTIC PROGRAMMING
PROBLEMS 206
6.1 Classes of convex concave game problems 206
6.2 MD methods of solving games: the case of a deterministic
oracle 210
6.3 MD methods of solving games: the case of a stochastic
oracle 219
Contents vii
6.4 Solution of convex operator inequalities 225
6.5 Solution of extremal problems with operator constraints 233
6.6 Solution of constrained stochastic problems 241
6.7 Complex stochastic programming problems 248
7 STRONGLY CONVEX PROBLEMS 254
7.1 Classes of smooth and strongly convex extremal problems 254
7.2 Quadratic programming and lower bounds of the com¬
plexity of strongly convex classes 261
7.3 Strongly convex programming; unconstrained problems 272
7.4 Minimax problems 277
7.5 Solution of constrained strongly convex and smooth
problems 285
7.6 Proof of Theorem 7.4.3 294
8 EFFICIENCY OF STANDARD
METHODS OF STRONGLY CONVEX
PROGRAMMING 307
8.1 On standard methods of strongly convex programming 307
8.2 The Fletcher Reeves method 313
8.3 The Polak Ribiere method 319
8.4 The Zoutendijk projection method 327
8.5 Remarks on the Davidon Fletcher Powell method 330
9 CONVEX PROGRAMMING
METHODS OF ZEROTH ORDER 333
9.1 Methods of zeroth order: deterministic oracle. I 334
9.2 Methods of zeroth order: deterministic oracle. II 341
9.3 Methods of zeroth order: stochastic oracle. I 349
9.4 Methods of zeroth order: stochastic oracle. II 354
viii Contents
APPENDIX: MATHEMATICAL
SUPPLEMENT 362
A. 1 Polish spaces, Borel functions, measures 362
A.2 Banach spaces 369
PRINCIPAL NOTATION 376
REFERENCES 380
INDEX 383
|
| any_adam_object | 1 |
| author | Nemirovskij, Arkadij S. 1947- Judin, David B. 1919-2006 |
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| id | DE-604.BV000212075 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:10:28Z |
| institution | BVB |
| isbn | 0471103454 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-000125412 |
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| physical | XV, 388 S. |
| psigel | TUB-nveb |
| publishDate | 1983 |
| publishDateSearch | 1983 |
| publishDateSort | 1983 |
| publisher | Wiley |
| record_format | marc |
| series2 | Wiley-Interscience series in discrete mathematics A Wiley-Interscience publication |
| spelling | Nemirovskij, Arkadij S. 1947- Verfasser (DE-588)12209395X aut Složnost' zadač i ėffektivnost' metodov optimizacii Problem complexity and method efficiency in optimization A. S. Nemirovsky ; D. B. Yudin Chichester u.a. Wiley 1983 XV, 388 S. txt rdacontent n rdamedia nc rdacarrier Wiley-Interscience series in discrete mathematics A Wiley-Interscience publication Aus dem Russ. übers. Optimierung (DE-588)4043664-0 gnd rswk-swf Optimierung (DE-588)4043664-0 s DE-604 Judin, David B. 1919-2006 Verfasser (DE-588)172172853 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000125412&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Nemirovskij, Arkadij S. 1947- Judin, David B. 1919-2006 Problem complexity and method efficiency in optimization Optimierung (DE-588)4043664-0 gnd |
| subject_GND | (DE-588)4043664-0 |
| title | Problem complexity and method efficiency in optimization |
| title_alt | Složnost' zadač i ėffektivnost' metodov optimizacii |
| title_auth | Problem complexity and method efficiency in optimization |
| title_exact_search | Problem complexity and method efficiency in optimization |
| title_full | Problem complexity and method efficiency in optimization A. S. Nemirovsky ; D. B. Yudin |
| title_fullStr | Problem complexity and method efficiency in optimization A. S. Nemirovsky ; D. B. Yudin |
| title_full_unstemmed | Problem complexity and method efficiency in optimization A. S. Nemirovsky ; D. B. Yudin |
| title_short | Problem complexity and method efficiency in optimization |
| title_sort | problem complexity and method efficiency in optimization |
| topic | Optimierung (DE-588)4043664-0 gnd |
| topic_facet | Optimierung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000125412&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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