Principles of optimization theory:
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Harrow
Alpha Science International
2005
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIV, 224 S. |
| ISBN: | 1842651668 |
Internformat
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Datensatz im Suchindex
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| adam_text | PRINCIPLES OF OPTIMIZATION THEORY C R BECTOR S CHANDRA J DUTTA ALPHA
SCIENCE INTERNATIONAL LTD. HARROW, U.K. CONTENTS FOREWORD VII PREFACE IX
ACKNOWLEDGEMENTS XI LIST OFFIGURES XV LIST OF SYMBOLS XVII 1
INTRODUCTION AND BASIC FACTS 1 1.1 OPTIMIZATION : A LITTLE HISTORY 1 1.2
BASIC FACTS AND DEFINITIONS 4 1.3 CONDITIONS FOR A MINIMUM 16 2 ELEMENTS
OF CONVEX ANALYSIS 19 2.1 CONVEX SETS AND SEPARATION THEOREMS 2.2
POLYHEDRAL CONVEX SETS AND FARKAS LEMMA 27 2.3 CONVEX FUNCTIONS : BASIC
PROPERTIES AND GENERALIZATIONS 29 2.4 SUBDIFFERENTIALS AND CALCULUS
RULES 56 2.5 TANGENT CONES AND NORMAL CONES 65 2.6 THEOREMS OFTHE
ALTERNATIVE 74 3 KARUSH-KUHN-TUCKER CONDITIONS 79 3.1 UNCONSTRAINED
MINIMIZATION 79 3.2 FRITZ JOHN CONDITIONS 82 3.3 KARUSH-KUHN-TUCKER
CONDITIONS 95 3.5 GENERALIZED CONVEXITY AND SUFFICIENCY 100 3.5 MIXED
CONSTRAINTS 104 3.6 *SECOND ORDER CONDITIONS 107 4 CONVEX OPTIMIZATION
115 4.1 THE BASIC PROBLEM 115 4.2 CONVEX OPTIMIZATION WITH INEQUALITY
CONSTRAINTS 118 4.3 SADDLE POINT CONDITIONS 126 4.4 CONVEX OPTIMIZATION
WITH MIXED CONSTRAINTS . 128 XIV 5 NONSMOOTH OPTIMIZATION... 133 5.1
CLARKE SUBDIFFERENTIAL AND RELATED RESUEUEZ 133 151 5.2 CLARKE TANGENT
AND NORMAL CONES 5.3 OPTIMALITY CONDITIONS IN LIPSCHITZOPTIMIZAEUEOEN . 154
5.5 *0 =J -- - - -NESS 162 5.4 GENERALIZED CONVEXITY AND NONSMOOTHR 189
5 6 *.UF F E R E N T I A L S AND P TIMA TY CONDITIONS. 170 5.6 *SUB DL
FFERENTIALS OF NON-LIPSCHITZ FUNCTIONS : SOME IDEAS 178 6 DUALITY THEORY
6.1 INTRODUCTION 6-2 LAGRANGIAN DUALITY I* NONLINEA^P^GRAMMMG. 186 6.3
CONJUGATE DUALITY IN CONVEX PROGRAMMING.... 6.4 EQMVALENCE OF FENCHEL
AND LAGRANGIAN DUALITY . 200 7 MONOTONE MAPS 7.1 INTRODUCTION 7.2
CONVEXITY AND MONOTONICITY 2Q G 7.3 SUBDIFFERENTIAL AND
MONOTONICITY..... . 207 7.4 QUASIMONOTONE AND PSEUDOMONOTONE MAPS 209
BIBLIOGRAPHY.. 271 INDEX 222
|
| adam_txt |
PRINCIPLES OF OPTIMIZATION THEORY C R BECTOR S CHANDRA J DUTTA ALPHA
SCIENCE INTERNATIONAL LTD. HARROW, U.K. CONTENTS FOREWORD VII PREFACE IX
ACKNOWLEDGEMENTS XI LIST OFFIGURES XV LIST OF SYMBOLS XVII 1
INTRODUCTION AND BASIC FACTS 1 1.1 OPTIMIZATION : A LITTLE HISTORY 1 1.2
BASIC FACTS AND DEFINITIONS 4 1.3 CONDITIONS FOR A MINIMUM 16 2 ELEMENTS
OF CONVEX ANALYSIS 19 2.1 CONVEX SETS AND SEPARATION THEOREMS 2.2
POLYHEDRAL CONVEX SETS AND FARKAS LEMMA 27 2.3 CONVEX FUNCTIONS : BASIC
PROPERTIES AND GENERALIZATIONS 29 2.4 SUBDIFFERENTIALS AND CALCULUS
RULES 56 2.5 TANGENT CONES AND NORMAL CONES 65 2.6 THEOREMS OFTHE
ALTERNATIVE 74 3 KARUSH-KUHN-TUCKER CONDITIONS 79 3.1 UNCONSTRAINED
MINIMIZATION 79 3.2 FRITZ JOHN CONDITIONS 82 3.3 KARUSH-KUHN-TUCKER
CONDITIONS 95 3.5 GENERALIZED CONVEXITY AND SUFFICIENCY 100 3.5 MIXED
CONSTRAINTS 104 3.6 *SECOND ORDER CONDITIONS 107 4 CONVEX OPTIMIZATION
115 4.1 THE BASIC PROBLEM 115 4.2 CONVEX OPTIMIZATION WITH INEQUALITY
CONSTRAINTS 118 4.3 SADDLE POINT CONDITIONS 126 4.4 CONVEX OPTIMIZATION
WITH MIXED CONSTRAINTS . 128 XIV 5 NONSMOOTH OPTIMIZATION. 133 5.1
CLARKE SUBDIFFERENTIAL AND RELATED RESUEUEZ"" 133 151 5.2 CLARKE TANGENT
AND NORMAL CONES 5.3 OPTIMALITY CONDITIONS IN LIPSCHITZOPTIMIZAEUEOEN'. 154
5.5 *0 =J"-- - - -NESS 162 5.4 GENERALIZED CONVEXITY AND NONSMOOTHR 189
5 6 *.UF F E R E N T I A L S AND P TIMA TY CONDITIONS. 170 5.6 *SUB DL
FFERENTIALS OF NON-LIPSCHITZ FUNCTIONS : SOME IDEAS 178 6 DUALITY THEORY
6.1 INTRODUCTION 6-2 LAGRANGIAN DUALITY I* NONLINEA^P^GRAMMMG.' 186 6.3
CONJUGATE DUALITY IN CONVEX PROGRAMMING. 6.4 EQMVALENCE OF FENCHEL
AND LAGRANGIAN DUALITY . 200 7 MONOTONE MAPS 7.1 INTRODUCTION 7.2
CONVEXITY AND MONOTONICITY 2Q G 7.3 SUBDIFFERENTIAL AND
MONOTONICITY.".' 207 7.4 QUASIMONOTONE AND PSEUDOMONOTONE MAPS 209
BIBLIOGRAPHY. 271 INDEX " 222 |
| any_adam_object | 1 |
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| dewey-full | 519.6 |
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| dewey-ones | 519 - Probabilities and applied mathematics |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
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| institution | BVB |
| isbn | 1842651668 |
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| spelling | Bector, C. R. Verfasser aut Principles of optimization theory C. R. Bector ; S. Chandra ; J. Dutta Harrow Alpha Science International 2005 XIV, 224 S. txt rdacontent n rdamedia nc rdacarrier Mathematical optimization Maxima and minima Optimierung (DE-588)4043664-0 gnd rswk-swf Optimierung (DE-588)4043664-0 s DE-604 Chandra, Suresh Verfasser aut Dutta, Jayasri Verfasser aut GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016785525&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bector, C. R. Chandra, Suresh Dutta, Jayasri Principles of optimization theory Mathematical optimization Maxima and minima Optimierung (DE-588)4043664-0 gnd |
| subject_GND | (DE-588)4043664-0 |
| title | Principles of optimization theory |
| title_auth | Principles of optimization theory |
| title_exact_search | Principles of optimization theory |
| title_exact_search_txtP | Principles of optimization theory |
| title_full | Principles of optimization theory C. R. Bector ; S. Chandra ; J. Dutta |
| title_fullStr | Principles of optimization theory C. R. Bector ; S. Chandra ; J. Dutta |
| title_full_unstemmed | Principles of optimization theory C. R. Bector ; S. Chandra ; J. Dutta |
| title_short | Principles of optimization theory |
| title_sort | principles of optimization theory |
| topic | Mathematical optimization Maxima and minima Optimierung (DE-588)4043664-0 gnd |
| topic_facet | Mathematical optimization Maxima and minima Optimierung |
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