Foundations of bilevel programming
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht [u.a.]
Kluwer
2002
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| Schriftenreihe: | Nonconvex optimization and its applications
61 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
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MARC
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| 100 | 1 | |a Dempe, Stephan |d 1956- |e Verfasser |0 (DE-588)132163535 |4 aut | |
| 245 | 1 | 0 | |a Foundations of bilevel programming |c by Stephan Dempe |
| 264 | 1 | |a Dordrecht [u.a.] |b Kluwer |c 2002 | |
| 300 | |a VIII, 306 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 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 |
| 689 | 0 | 0 | |a Hierarchische Optimierung |0 (DE-588)4300608-5 |D s |
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| 830 | 0 | |a Nonconvex optimization and its applications |v 61 |w (DE-604)BV010085908 |9 61 | |
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| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-009879817 | |
Datensatz im Suchindex
| DE-BY-TUM_call_number | 0002 MAT 910f 2012 A 978 |
|---|---|
| DE-BY-TUM_katkey | 1812592 |
| DE-BY-TUM_location | 00 |
| DE-BY-TUM_media_number | 040007570238 |
| _version_ | 1820858141075570688 |
| 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
|
| any_adam_object | 1 |
| author | Dempe, Stephan 1956- |
| author_GND | (DE-588)132163535 |
| author_facet | Dempe, Stephan 1956- |
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| author_sort | Dempe, Stephan 1956- |
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| classification_tum | MAT 490f MAT 910f |
| ctrlnum | (OCoLC)49681354 (DE-599)BVBBV014486837 |
| dewey-full | 519.7 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.7 |
| dewey-search | 519.7 |
| dewey-sort | 3519.7 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| format | Book |
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| id | DE-604.BV014486837 |
| illustrated | Illustrated |
| indexdate | 2024-12-23T15:56:56Z |
| institution | BVB |
| isbn | 1402006314 9781402006319 9781441952202 |
| language | English |
| lccn | 2002069409 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009879817 |
| oclc_num | 49681354 |
| open_access_boolean | |
| owner | DE-20 DE-29T DE-384 DE-91 DE-BY-TUM DE-N2 DE-83 |
| owner_facet | DE-20 DE-29T DE-384 DE-91 DE-BY-TUM DE-N2 DE-83 |
| physical | VIII, 306 S. graph. Darst. |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | Kluwer |
| record_format | marc |
| series | Nonconvex optimization and its applications |
| series2 | Nonconvex optimization and its applications |
| 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 |
| volume_link | (DE-604)BV010085908 |
| work_keys_str_mv | AT dempestephan foundationsofbilevelprogramming |