Holdings: Vector optimization

Vector optimization: theory, applications, and extensions ; with 14 tables

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Bibliographic Details
Main Author:	Jahn, Johannes 1951- (Author)
Format:	Book
Language:	English
Published:	Heidelberg [u.a.] Springer 2011
Edition:	2. ed.
Subjects:	Mehrkriterielle Optimierung
Online Access:	Inhaltsverzeichnis
Physical Description:	XV, 481 S. Ill., graph. Darst.
ISBN:	9783642170041

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MARC


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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
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spelling	Jahn, Johannes 1951- Verfasser (DE-588)104274905 aut Vector optimization theory, applications, and extensions ; with 14 tables Johannes Jahn 2. ed. Heidelberg [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-604 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022482521&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Jahn, Johannes 1951- Vector optimization theory, applications, and extensions ; with 14 tables Mehrkriterielle Optimierung (DE-588)4610682-0 gnd
subject_GND	(DE-588)4610682-0
title	Vector optimization theory, applications, and extensions ; with 14 tables
title_auth	Vector optimization theory, applications, and extensions ; with 14 tables
title_exact_search	Vector optimization theory, applications, and extensions ; with 14 tables
title_full	Vector optimization theory, applications, and extensions ; with 14 tables Johannes Jahn
title_fullStr	Vector optimization theory, applications, and extensions ; with 14 tables Johannes Jahn
title_full_unstemmed	Vector optimization theory, applications, and extensions ; with 14 tables Johannes Jahn
title_short	Vector optimization
title_sort	vector optimization theory applications and extensions with 14 tables
title_sub	theory, applications, and extensions ; with 14 tables
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=022482521&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
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