Foundations of bilevel programming:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht [u.a.]
Kluwer
2002
|
| Schriftenreihe: | Nonconvex optimization and its applications
61 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references (p. 283-302) and index. - Hier auch später erchienene, unveränderte Nachdrucke |
| Beschreibung: | VIII, 306 S. graph. Darst. |
| ISBN: | 1402006314 9781402006319 9781441952202 |
Internformat
MARC
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| 245 | 1 | 0 | |a Foundations of bilevel programming |c by Stephan Dempe |
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| 300 | |a VIII, 306 S. |b graph. Darst. | ||
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| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Nonconvex optimization and its applications |v 61 | |
| 500 | |a Includes bibliographical references (p. 283-302) and index. - Hier auch später erchienene, unveränderte Nachdrucke | ||
| 650 | 4 | |a Optimisation mathématique | |
| 650 | 7 | |a Programação hierárquica |2 larpcal | |
| 650 | 7 | |a Programação matemática |2 larpcal | |
| 650 | 4 | |a Programmation (Mathématiques) | |
| 650 | 4 | |a Mathematical optimization | |
| 650 | 4 | |a Programming (Mathematics) | |
| 650 | 0 | 7 | |a Parametrische Optimierung |0 (DE-588)4044615-3 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Hierarchische Optimierung |0 (DE-588)4300608-5 |2 gnd |9 rswk-swf |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-009879817 | ||
Datensatz im Suchindex
| _version_ | 1804129305869942784 |
|---|---|
| adam_text | Contents
1. INTRODUCTION 1
2. APPLICATIONS 7
2.1 Stackelberg games 7
2.2 Optimal chemical equilibria 11
2.3 Environmental economics 12
2.4 Discrimination between sets 15
2.5 Further applications 18
3. LINEAR BILEVEL PROBLEMS 21
3.1 The model and one example 21
3.2 The geometric nature of linear bilevel programming 24
3.3 Existence of optimal solutions 27
3.4 Relations to other MP problems 31
3.5 Optimality conditions 36
3.6 Solution algorithms 47
3.7 Proofs 56
4. PARAMETRIC OPTIMIZATION 61
4.1 Optimality conditions 62
4.2 Upper semicontinuity of the solution set mapping 64
4.3 Piecewise continuously differentiable functions 70
4.4 Properties of optimal solutions 75
4.5 Properties of the optimal value function 88
4.6 Proofs 91
5. OPTIMALITY CONDITIONS 119
5.1 Optimality concepts 121
5.2 Optimality conditions based on strong stability 129
5.3 The contingent cone to the feasible set 135
5.4 Regularity 145
v
vi FOUNDATIONS OF B1LEVEL PROGRAMMING
5.5 Optimality conditions using the KKT reformulation 149
5.6 The approach via the lower level optimal value function 155
5.7 Generalized PC1 functions 158
5.8 Proofs 172
6. SOLUTION ALGORITHMS 193
6.1 A descent algorithm 194
6.2 A bundle algorithm 200
6.3 Penalty methods 209
6.4 A trust region method 211
6.5 Smoothing methods 215
7. NONUNIQUE LOWER LEVEL SOLUTION 217
7.1 Approximation of desired solutions 218
7.2 Stability of bilevel problems 226
7.3 Special perturbations 230
7.4 Proofs 243
8. DISCRETE BILEVEL PROBLEMS 255
8.1 Two introductory examples 255
8.2 Cutting plane algorithm 258
8.3 Inner approximation 264
8.4 Knapsack lower level problems 266
8.5 Proofs 275
REFERENCES 283
Notations 303
Index
305
|
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| discipline | Mathematik Wirtschaftswissenschaften |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T19:03:02Z |
| institution | BVB |
| isbn | 1402006314 9781402006319 9781441952202 |
| language | English |
| lccn | 2002069409 |
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| physical | VIII, 306 S. graph. Darst. |
| publishDate | 2002 |
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| publisher | Kluwer |
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| series | Nonconvex optimization and its applications |
| series2 | Nonconvex optimization and its applications |
| spelling | Dempe, Stephan 1956- Verfasser (DE-588)132163535 aut Foundations of bilevel programming by Stephan Dempe Dordrecht [u.a.] Kluwer 2002 VIII, 306 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Nonconvex optimization and its applications 61 Includes bibliographical references (p. 283-302) and index. - Hier auch später erchienene, unveränderte Nachdrucke Optimisation mathématique Programação hierárquica larpcal Programação matemática larpcal Programmation (Mathématiques) Mathematical optimization Programming (Mathematics) Parametrische Optimierung (DE-588)4044615-3 gnd rswk-swf Hierarchische Optimierung (DE-588)4300608-5 gnd rswk-swf Hierarchische Optimierung (DE-588)4300608-5 s DE-604 Parametrische Optimierung (DE-588)4044615-3 s Erscheint auch als Online-Ausgabe 978-0-306-48045-4 Nonconvex optimization and its applications 61 (DE-604)BV010085908 61 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009879817&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Dempe, Stephan 1956- Foundations of bilevel programming Nonconvex optimization and its applications Optimisation mathématique Programação hierárquica larpcal Programação matemática larpcal Programmation (Mathématiques) Mathematical optimization Programming (Mathematics) Parametrische Optimierung (DE-588)4044615-3 gnd Hierarchische Optimierung (DE-588)4300608-5 gnd |
| subject_GND | (DE-588)4044615-3 (DE-588)4300608-5 |
| title | Foundations of bilevel programming |
| title_auth | Foundations of bilevel programming |
| title_exact_search | Foundations of bilevel programming |
| title_full | Foundations of bilevel programming by Stephan Dempe |
| title_fullStr | Foundations of bilevel programming by Stephan Dempe |
| title_full_unstemmed | Foundations of bilevel programming by Stephan Dempe |
| title_short | Foundations of bilevel programming |
| title_sort | foundations of bilevel programming |
| topic | Optimisation mathématique Programação hierárquica larpcal Programação matemática larpcal Programmation (Mathématiques) Mathematical optimization Programming (Mathematics) Parametrische Optimierung (DE-588)4044615-3 gnd Hierarchische Optimierung (DE-588)4300608-5 gnd |
| topic_facet | Optimisation mathématique Programação hierárquica Programação matemática Programmation (Mathématiques) Mathematical optimization Programming (Mathematics) Parametrische Optimierung Hierarchische Optimierung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009879817&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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