Vector optimization: theory, applications, and extensions
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2011
|
| Edition: | 2. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XV, 481 S. Ill., graph. Darst. |
| ISBN: | 9783642170041 9783642170058 |
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MARC
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| 245 | 1 | 0 | |a Vector optimization |b theory, applications, and extensions |c Johannes Jahn |
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Record in the Search Index
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| adam_text | IMAGE 1
CONTENTS
PREFACE VII
CONVEX ANALYSIS 1
LINEAR SPACES 3
1.1 LINEAR SPACES AND CONVEX SETS 3
1.2 PARTIALLY ORDERED LINEAR SPACES 12
1.3 TOPOLOGICAL LINEAR SPACES 21
1.4 SOME EXAMPLES 32
NOTES 35
MAPS ON LINEAR SPACES 37
2.1 CONVEX MAPS 37
2.2 DIFFERENTIATE MAPS 45
NOTES 59
SOME FUNDAMENTAL THEOREMS 61
3.1 ZORN S LEMMA AND THE HAHN-BANACH THEOREM 61 3.2 SEPARATION THEOREMS
71
3.3 A JAMES THEOREM 81
3.4 TWO KREIN-RUTMAN THEOREMS 87
3.5 CONTINGENT CONES AND A LYUSTERNIK THEOREM 90 NOTES 99
XI
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/1009237616
DIGITALISIERT DURCH
IMAGE 2
XII CONTENTS
II THEORY OF VECTOR OPTIMIZATION 101
4 OPTIMALITY NOTIONS 103
NOTES 113
5 SCALARIZATION 115
5.1 NECESSARY CONDITIONS FOR OPTIMAL ELEMENTS OF A SET . .115 5.2
SUFFICIENT CONDITIONS FOR OPTIMAL ELEMENTS OF A SET . . 129 5.3
PARAMETRIC APPROXIMATION PROBLEMS 139
NOTES 147
6 EXISTENCE THEOREMS 149
NOTES 159
7 GENERALIZED LAGRANGE MULTIPLIER RULE 161
7. 1 NECESSARY CONDITIONS FOR MINIMAL AND WEAKLY MINIMAL ELEMENTS 161
7.2 SUFFICIENT CONDITIONS FOR MINIMAL AND WEAKLY MINIMAL ELEMENTS 174
7.2.1 GENERALIZED QUASICONVEX MAPS 174
7.2.2 SUFFICIENCY OF THE GENERALIZED MULTIPLIER RULE . 181 NOTES 187
8 DUALITY 189
8.1 A GENERAL DUALITY PRINCIPLE 189
8.2 DUALITY THEOREMS FOR ABSTRACT OPTIMIZATION PROBLEMS 192 8.3
SPECIALIZATION TO ABSTRACT LINEAR OPTIMIZATION PROBLEMS200 NOTES 207
III MATHEMATICAL APPLICATIONS 209
9 VECTOR APPROXIMATION 211
9.1 INTRODUCTION 211
9.2 SIMULTANEOUS APPROXIMATION 213
9.3 GENERALIZED KOLMOGOROV CONDITION 216
9.4 NONLINEAR CHEBYSHEV VECTOR APPROXIMATION 218 9.5 LINEAR CHEBYSHEV
VECTOR APPROXIMATION 226
IMAGE 3
CONTENTS XIII
9.5.1 DUALITY RESULTS 227
9.5.2 AN ALTERNATION THEOREM 233
NOTES 241
10 COOPERATIVE N PLAYER DIFFERENTIAL GAMES 243
10.1 BASIC REMARKS ON THE COOPERATION CONCEPT 243 10.2 A MAXIMUM
PRINCIPLE 245
10.2.1 NECESSARY CONDITIONS FOR OPTIMAL AND WEAKLY OPTIMAL CONTROLS 247
10.2.2 SUFFICIENT CONDITIONS FOR OPTIMAL AND WEAKLY OPTIMAL CONTROLS 259
10.3 A SPECIAL COOPERATIVE N PLAYER DIFFERENTIAL GAME . . . 270 NOTES
277
IV ENGINEERING APPLICATIONS 279
11 THEORETICAL BASICS OF MULTIOBJECTIVE OPTIMIZATION 281 11.1 BASIC
CONCEPTS 281
11.2 SPECIAL SCALARIZATION RESULTS 291
11.2.1 WEIGHTED SUM APPROACH 292
11.2.2 WEIGHTED CHEBYSHEV NORM APPROACH 304 11.2.3 SPECIAL SCALAR
PROBLEMS 307
NOTES 311
12 NUMERICAL METHODS 315
12.1 MODIFIED POLAK METHOD 315
12.2 EICHFELDER-POLAK METHOD 321
12.3 INTERACTIVE METHODS 325
12.3.1 MODIFIED STEM METHOD 326
12.3.2 METHOD OF REFERENCE POINT APPROXIMATION . . . 330 THE LINEAR CASE
332
THE BICRITERIAL NONLINEAR CASE 337
12.4 METHOD FOR DISCRETE PROBLEMS 343
NOTES 348
IMAGE 4
XIV CONTENTS
13 MULTIOBJECTIVE DESIGN PROBLEMS 351
13.1 DESIGN OF ANTENNAS 352
13.2 DESIGN OF FDDI COMPUTER NETWORKS 359
13.2.1 A COOPERATIVE GAME 360
13.2.2 MINIMIZATION OF MEAN WAITING TIMES 362
13.2.3 NUMERICAL RESULTS 365
13.3 FLUIDIZED REACTOR-HEATER SYSTEM 367
13.3.1 SIMPLIFICATION OF THE CONSTRAINTS 369
13.3.2 NUMERICAL RESULTS 371
13.4 A CROSS-CURRENT MULTISTAGE EXTRACTION PROCESS . . .. 373 13.5 FIELD
DESIGN OF A MAGNETIC RESONANCE SYSTEM 376 NOTES 380
V EXTENSIONS TO SET OPTIMIZATION 383
14 BASIC CONCEPTS AND RESULTS OF SET OPTIMIZATION 385 NOTES 391
15 CONTINGENT EPIDERIVATIVES 393
15.1 CONTINGENT DERIVATIVES AND CONTINGENT EPIDERIVATIVES . 393 15.2
PROPERTIES OF CONTINGENT EPIDERIVATIVES 397
15.3 CONTINGENT EPIDERIVATIVES OF REAL-VALUED FUNCTIONS . . 401 15.4
GENERALIZED CONTINGENT EPIDERIVATIVES 405
NOTES 409
16 SUBDIFFERENTIAL 411
16.1 CONCEPT OF SUBDIFFERENTIAL 411
16.2 PROPERTIES OF THE SUBDIFFERENTIAL 413
16.3 WEAK SUBGRADIENTS 417
NOTES 421
17 OPTIMALITY CONDITIONS 423
17.1 OPTIMALITY CONDITIONS WITH CONTINGENT EPIDERIVATIVES . 423 17.2
OPTIMALITY CONDITIONS WITH SUBGRADIENTS 428
17.3 OPTIMALITY CONDITIONS WITH WEAK SUBGRADIENTS . . .. 429 17.4
GENERALIZED LAGRANGE MULTIPLIER RULE 431
17.4.1 A NECESSARY OPTIMALITY CONDITION 432
IMAGE 5
CONTENTS XV
17.4.2 A SUFFICIENT OPTIMALITY CONDITION 441
NOTES 446
BIBLIOGRAPHY 449
LIST OF SYMBOLS 475
INDEX 477
|
| any_adam_object | 1 |
| author | Jahn, Johannes |
| author_facet | Jahn, Johannes |
| author_role | aut |
| author_sort | Jahn, Johannes |
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| building | Verbundindex |
| bvnumber | BV037385468 |
| ctrlnum | (OCoLC)873729099 (DE-599)BVBBV037385468 |
| dewey-full | 519.7 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.7 |
| dewey-search | 519.7 |
| dewey-sort | 3519.7 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV037385468 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T23:23:10Z |
| institution | BVB |
| isbn | 9783642170041 9783642170058 |
| language | English |
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| physical | XV, 481 S. Ill., graph. Darst. |
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| spelling | Jahn, Johannes Verfasser aut Vector optimization theory, applications, and extensions Johannes Jahn 2. ed. Berlin [u.a.] Springer 2011 XV, 481 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mehrkriterielle Optimierung (DE-588)4610682-0 gnd rswk-swf Mehrkriterielle Optimierung (DE-588)4610682-0 s DE-101 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022538500&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Jahn, Johannes Vector optimization theory, applications, and extensions Mehrkriterielle Optimierung (DE-588)4610682-0 gnd |
| subject_GND | (DE-588)4610682-0 |
| title | Vector optimization theory, applications, and extensions |
| title_auth | Vector optimization theory, applications, and extensions |
| title_exact_search | Vector optimization theory, applications, and extensions |
| title_full | Vector optimization theory, applications, and extensions Johannes Jahn |
| title_fullStr | Vector optimization theory, applications, and extensions Johannes Jahn |
| title_full_unstemmed | Vector optimization theory, applications, and extensions Johannes Jahn |
| title_short | Vector optimization |
| title_sort | vector optimization theory applications and extensions |
| title_sub | theory, applications, and extensions |
| topic | Mehrkriterielle Optimierung (DE-588)4610682-0 gnd |
| topic_facet | Mehrkriterielle Optimierung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022538500&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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