Foundations of Bilevel Programming:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Boston, MA
Springer US
2002
|
| Schriftenreihe: | Nonconvex Optimization and Its Applications
61 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | Bilevel programming problems are hierarchical optimization problems where the constraints of one problem (the so-called upper level problem) are defined in part by a second parametric optimization problem (the lower level problem). If the lower level problem has a unique optimal solution for all parameter values, this problem is equivalent to a one-level optimization problem having an implicitly defined objective function. Special emphasize in the book is on problems having non-unique lower level optimal solutions, the optimistic (or weak) and the pessimistic (or strong) approaches are discussed. The book starts with the required results in parametric nonlinear optimization. This is followed by the main theoretical results including necessary and sufficient optimality conditions and solution algorithms for bilevel problems. Stationarity conditions can be applied to the lower level problem to transform the optimistic bilevel programming problem into a one-level problem. Properties of the resulting problem are highlighted and its relation to the bilevel problem is investigated. Stability properties, numerical complexity, and problems having additional integrality conditions on the variables are also discussed. Audience: Applied mathematicians and economists working in optimization, operations research, and economic modelling. Students interested in optimization will also find this book useful |
| Beschreibung: | 1 Online-Ressource (VIII, 309 p) |
| ISBN: | 9780306480454 9781402006319 |
| ISSN: | 1571-568X |
| DOI: | 10.1007/b101970 |
Internformat
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| 500 | |a Bilevel programming problems are hierarchical optimization problems where the constraints of one problem (the so-called upper level problem) are defined in part by a second parametric optimization problem (the lower level problem). If the lower level problem has a unique optimal solution for all parameter values, this problem is equivalent to a one-level optimization problem having an implicitly defined objective function. Special emphasize in the book is on problems having non-unique lower level optimal solutions, the optimistic (or weak) and the pessimistic (or strong) approaches are discussed. The book starts with the required results in parametric nonlinear optimization. This is followed by the main theoretical results including necessary and sufficient optimality conditions and solution algorithms for bilevel problems. Stationarity conditions can be applied to the lower level problem to transform the optimistic bilevel programming problem into a one-level problem. Properties of the resulting problem are highlighted and its relation to the bilevel problem is investigated. Stability properties, numerical complexity, and problems having additional integrality conditions on the variables are also discussed. Audience: Applied mathematicians and economists working in optimization, operations research, and economic modelling. Students interested in optimization will also find this book useful | ||
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Datensatz im Suchindex
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|---|---|
| any_adam_object | |
| author | Dempe, Stephan |
| author_facet | Dempe, Stephan |
| author_role | aut |
| author_sort | Dempe, Stephan |
| author_variant | s d sd |
| building | Verbundindex |
| bvnumber | BV042418886 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)879623356 (DE-599)BVBBV042418886 |
| dewey-full | 515.64 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.64 |
| dewey-search | 515.64 |
| dewey-sort | 3515.64 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/b101970 |
| format | Electronic eBook |
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| id | DE-604.BV042418886 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:03Z |
| institution | BVB |
| isbn | 9780306480454 9781402006319 |
| issn | 1571-568X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027854303 |
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| physical | 1 Online-Ressource (VIII, 309 p) |
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| publishDate | 2002 |
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| series2 | Nonconvex Optimization and Its Applications |
| spelling | Dempe, Stephan Verfasser aut Foundations of Bilevel Programming by Stephan Dempe Boston, MA Springer US 2002 1 Online-Ressource (VIII, 309 p) txt rdacontent c rdamedia cr rdacarrier Nonconvex Optimization and Its Applications 61 1571-568X Bilevel programming problems are hierarchical optimization problems where the constraints of one problem (the so-called upper level problem) are defined in part by a second parametric optimization problem (the lower level problem). If the lower level problem has a unique optimal solution for all parameter values, this problem is equivalent to a one-level optimization problem having an implicitly defined objective function. Special emphasize in the book is on problems having non-unique lower level optimal solutions, the optimistic (or weak) and the pessimistic (or strong) approaches are discussed. The book starts with the required results in parametric nonlinear optimization. This is followed by the main theoretical results including necessary and sufficient optimality conditions and solution algorithms for bilevel problems. Stationarity conditions can be applied to the lower level problem to transform the optimistic bilevel programming problem into a one-level problem. Properties of the resulting problem are highlighted and its relation to the bilevel problem is investigated. Stability properties, numerical complexity, and problems having additional integrality conditions on the variables are also discussed. Audience: Applied mathematicians and economists working in optimization, operations research, and economic modelling. Students interested in optimization will also find this book useful Mathematics Mathematical optimization Calculus of Variations and Optimal Control; Optimization Operations Research/Decision Theory Optimization Mathematik 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 1\p DE-604 Parametrische Optimierung (DE-588)4044615-3 s 2\p DE-604 https://doi.org/10.1007/b101970 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Dempe, Stephan Foundations of Bilevel Programming Mathematics Mathematical optimization Calculus of Variations and Optimal Control; Optimization Operations Research/Decision Theory Optimization Mathematik 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 | Mathematics Mathematical optimization Calculus of Variations and Optimal Control; Optimization Operations Research/Decision Theory Optimization Mathematik Parametrische Optimierung (DE-588)4044615-3 gnd Hierarchische Optimierung (DE-588)4300608-5 gnd |
| topic_facet | Mathematics Mathematical optimization Calculus of Variations and Optimal Control; Optimization Operations Research/Decision Theory Optimization Mathematik Parametrische Optimierung Hierarchische Optimierung |
| url | https://doi.org/10.1007/b101970 |
| work_keys_str_mv | AT dempestephan foundationsofbilevelprogramming |