Introduction to the theory of nonlinear optimization:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2007
|
| Edition: | 3. ed. |
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Physical Description: | X, 292 S. Ill., graph. Darst. |
| ISBN: | 9783540493785 3540493786 |
Staff View
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Record in the Search Index
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|---|---|
| adam_text |
JOHANNES JAHN INTRODUCTION TO THE THEORY OF NONLINEAR OPTIMIZATION THIRD
EDITION WITH 31 FIGURES J SPRINGER CONTENTS PREFACE VII 1 INTRODUCTION
AND PROBLEM FORMULATION 1 2 EXISTENCE THEOREMS FOR MINIMAL POINTS 7 2.1
PROBLEM FORMULATION 7 2.2 EXISTENCE THEOREMS 8 2.3 SET OF MINIMAL POINTS
18 2.4 APPLICATION TO APPROXIMATION PROBLEMS 19 2.5 APPLICATION TO
OPTIMAL CONTROL PROBLEMS 23 EXERCISES 29 3 GENERALIZED DERIVATIVES 31
3.1 DIRECTIONAL DERIVATIVE 31 3.2 GATEAUX AND FRECHET DERIVATIVES 37 3.3
SUBDIFFERENTIAL 49 3.4 QUASIDIFFERENTIAL 57 3.5 CLARKE DERIVATIVE 67
EXERCISES 75 4 TANGENT CONES 79 4.1 DEFINITION AND PROPERTIES . . *. 79
4.2 OPTIMALITY CONDITIONS 88 4.3 A LYUSTERNIK THEOREM 95 EXERCISES 103 5
GENERALIZED LAGRANGE MULTIPLIER RULE 105 5.1 PROBLEM FORMULATION, 105 X
CONTENTS 5.2 NECESSARY OPTIMALITY CONDITIONS 108 5.3 SUFFICIENT
OPTIMALITY CONDITIONS 126 5.4 APPLICATION TO OPTIMAL CONTROL PROBLEMS
136 EXERCISES 156 6 DUALITY 159 6.1 PROBLEM FORMULATION 159 6.2 DUALITY
THEOREMS 164 6.3 SADDLE POINT THEOREMS 168 6.4 LINEAR PROBLEMS 172 6.5
APPLICATION TO APPROXIMATION PROBLEMS 175 EXERCISES 184 7 APPLICATION TO
EXTENDED SEMIDEFLNITE OPTIMIZATION 187 7.1 LOWNER ORDERING CONE AND
EXTENSIONS 187 7.2 OPTIMALITY CONDITIONS 202 7.3 DUALITY 207 EXERCISES
210 8 DIRECT TREATMENT OF SPECIAL OPTIMIZATION PROBLEMS 213 8.1 LINEAR
QUADRATIC OPTIMAL CONTROL PROBLEMS 213 8.2 TIME MINIMAL CONTROL PROBLEMS
221 EXERCISES 238 A WEAK CONVERGENCE 241 B REFLEXIVITY OF BANACH SPACES
243 C HAHN-BANACH THEOREM 245 D PARTIALLY ORDERED LINEAR SPACES 249
BIBLIOGRAPHY 253 ANSWERS TO THE EXERCISES 275 INDEX 289 |
| adam_txt |
JOHANNES JAHN INTRODUCTION TO THE THEORY OF NONLINEAR OPTIMIZATION THIRD
EDITION WITH 31 FIGURES J SPRINGER CONTENTS PREFACE VII 1 INTRODUCTION
AND PROBLEM FORMULATION 1 2 EXISTENCE THEOREMS FOR MINIMAL POINTS 7 2.1
PROBLEM FORMULATION 7 2.2 EXISTENCE THEOREMS 8 2.3 SET OF MINIMAL POINTS
18 2.4 APPLICATION TO APPROXIMATION PROBLEMS 19 2.5 APPLICATION TO
OPTIMAL CONTROL PROBLEMS 23 EXERCISES 29 3 GENERALIZED DERIVATIVES 31
3.1 DIRECTIONAL DERIVATIVE 31 3.2 GATEAUX AND FRECHET DERIVATIVES 37 3.3
SUBDIFFERENTIAL 49 3.4 QUASIDIFFERENTIAL 57 3.5 CLARKE DERIVATIVE 67
EXERCISES 75 4 TANGENT CONES 79 4.1 DEFINITION AND PROPERTIES . . *. 79
4.2 OPTIMALITY CONDITIONS 88 4.3 A LYUSTERNIK THEOREM 95 EXERCISES 103 5
GENERALIZED LAGRANGE MULTIPLIER RULE 105 5.1 PROBLEM FORMULATION, 105 X
CONTENTS 5.2 NECESSARY OPTIMALITY CONDITIONS 108 5.3 SUFFICIENT
OPTIMALITY CONDITIONS 126 5.4 APPLICATION TO OPTIMAL CONTROL PROBLEMS
136 EXERCISES 156 6 DUALITY 159 6.1 PROBLEM FORMULATION 159 6.2 DUALITY
THEOREMS 164 6.3 SADDLE POINT THEOREMS 168 6.4 LINEAR PROBLEMS 172 6.5
APPLICATION TO APPROXIMATION PROBLEMS 175 EXERCISES 184 7 APPLICATION TO
EXTENDED SEMIDEFLNITE OPTIMIZATION 187 7.1 LOWNER ORDERING CONE AND
EXTENSIONS 187 7.2 OPTIMALITY CONDITIONS 202 7.3 DUALITY 207 EXERCISES
210 8 DIRECT TREATMENT OF SPECIAL OPTIMIZATION PROBLEMS 213 8.1 LINEAR
QUADRATIC OPTIMAL CONTROL PROBLEMS 213 8.2 TIME MINIMAL CONTROL PROBLEMS
221 EXERCISES 238 A WEAK CONVERGENCE 241 B REFLEXIVITY OF BANACH SPACES
243 C HAHN-BANACH THEOREM 245 D PARTIALLY ORDERED LINEAR SPACES 249
BIBLIOGRAPHY 253 ANSWERS TO THE EXERCISES 275 INDEX 289 |
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| dewey-full | 519.6 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| edition | 3. ed. |
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| isbn | 9783540493785 3540493786 |
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| spelling | Jahn, Johannes 1951- Verfasser (DE-588)104274905 aut Introduction to the theory of nonlinear optimization Johannes Jahn 3. ed. Berlin [u.a.] Springer 2007 X, 292 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Niet-lineaire theorieën gtt Optimaliseren gtt Mathematical optimization Nonlinear theories Nichtlineare Optimierung (DE-588)4128192-5 gnd rswk-swf Nichtlineare Optimierung (DE-588)4128192-5 s DE-604 text/html http://deposit.dnb.de/cgi-bin/dokserv?id=2867076&prov=M&dok_var=1&dok_ext=htm Inhaltstext HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015462994&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
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| subject_GND | (DE-588)4128192-5 |
| title | Introduction to the theory of nonlinear optimization |
| title_auth | Introduction to the theory of nonlinear optimization |
| title_exact_search | Introduction to the theory of nonlinear optimization |
| title_exact_search_txtP | Introduction to the theory of nonlinear optimization |
| title_full | Introduction to the theory of nonlinear optimization Johannes Jahn |
| title_fullStr | Introduction to the theory of nonlinear optimization Johannes Jahn |
| title_full_unstemmed | Introduction to the theory of nonlinear optimization Johannes Jahn |
| title_short | Introduction to the theory of nonlinear optimization |
| title_sort | introduction to the theory of nonlinear optimization |
| topic | Niet-lineaire theorieën gtt Optimaliseren gtt Mathematical optimization Nonlinear theories Nichtlineare Optimierung (DE-588)4128192-5 gnd |
| topic_facet | Niet-lineaire theorieën Optimaliseren Mathematical optimization Nonlinear theories Nichtlineare Optimierung |
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