Introduction to the theory of nonlinear optimization:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin u.a.
Springer
1994
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | VIII, 249 S. graph. Darst. |
| ISBN: | 3540583203 0387583203 |
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| 245 | 1 | 0 | |a Introduction to the theory of nonlinear optimization |c Johannes Jahn |
| 264 | 1 | |a Berlin u.a. |b Springer |c 1994 | |
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Datensatz im Suchindex
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|---|---|
| adam_text | JOHANNES JAHN
INTRODUCTION
TO THE THEORY
OF NONLINEAR
OPTIMIZATION
WITH 30 FIGURES
SPRINGER-VERLAG
BERLIN HEIDELBERG NEW YORK
LONDON PARIS TOKYO
HONG KONG BARCELONA
BUDAPEST
CONTENTS
PREFACE V
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 ** APPROXIMATION PROBLEMS 19
2.5 APPLICATION TO OPTIMAL CONTROL PROBLEMS 24
EXERCISES 30
3 GENERALIZED DERIVATIVES 33
3.1 DIRECTIONAL DERIVATIVE 33
3.2 GATEAUX AND FRECHET DERIVATIVES 39
3.3 SUBDIFFERENTIAL 51
3.4 QUASIDIFFERENTIAL 59
3.5 CLARKE DERIVATIVE 69
EXERCISES 77
4 TANGENT CONES 81
4.1 DEFINITION AND PROPERTIES 81
4.2 OPTIMALITY CONDITIONS 91
4.3 A LYUSTERNIK THEOREM 98
EXERCISES 106
5 GENERALIZED LAGRANGE MULTIPLIER RULE 109
5.1 PROBLEM FORMULATION 109
VIII CONTENTS
5.2 NECESSARY OPTIMALITY CONDITIONS 112
5.3 SUFFICIENT OPTIMALITY CONDITIONS 130
5.4 APPLICATION TO OPTIMAL CONTROL PROBLEMS 140
EXERCISES 159
6 DUALITY 163
6.1 PROBLEM FORMULATION 163
6.2 DUALITY THEOREMS 168
6.3 SADDLE POINT THEOREMS 172
6.4 LINEAR PROBLEMS 176
6.5 APPLICATION TO APPROXIMATION PROBLEMS 179
EXERCISES 188
7 DIRECT TREATMENT OF SPECIAL OPTIMIZATION PROBLEMS 191
7.1 LINEAR QUADRATIC OPTIMAL CONTROL PROBLEMS 191
7.2 TIME MINIMAL CONTROL PROBLEMS 199
EXERCISES 216
A WEAK CONVERGENCE 219
8 REFLEXIVITY OF BANACH SPACES 221
* HAHN-BANACH THEOREM 223
D PARTIALLY ORDERED LINEAR SPACES 227
BIBLIOGRAPHY 231
INDEX 247
|
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| ctrlnum | (OCoLC)31044770 (DE-599)BVBBV009780044 |
| dewey-full | 519.7/6 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.7/6 |
| dewey-search | 519.7/6 |
| dewey-sort | 3519.7 16 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
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| institution | BVB |
| isbn | 3540583203 0387583203 |
| language | English |
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| physical | VIII, 249 S. graph. Darst. |
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| spelling | Jahn, Johannes 1951- Verfasser (DE-588)104274905 aut Introduction to the theory of nonlinear optimization Johannes Jahn Berlin u.a. Springer 1994 VIII, 249 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Optimaliseren gtt Optimisation mathématique ram Théories non-linéaires ram Mathematical optimization Nonlinear theories Nichtlineare Optimierung (DE-588)4128192-5 gnd rswk-swf Nichtlineare Optimierung (DE-588)4128192-5 s DE-604 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006471643&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Jahn, Johannes 1951- Introduction to the theory of nonlinear optimization Optimaliseren gtt Optimisation mathématique ram Théories non-linéaires ram Mathematical optimization Nonlinear theories Nichtlineare Optimierung (DE-588)4128192-5 gnd |
| 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_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 | Optimaliseren gtt Optimisation mathématique ram Théories non-linéaires ram Mathematical optimization Nonlinear theories Nichtlineare Optimierung (DE-588)4128192-5 gnd |
| topic_facet | Optimaliseren Optimisation mathématique Théories non-linéaires Mathematical optimization Nonlinear theories Nichtlineare Optimierung |
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