Foundations of Bilevel Programming (Hardcover)

Stephan Dempe

ISBN 10: 1402006314 / ISBN 13: 9781402006319

Editore: Kluwer Academic Publishers, New York, NY, 2002

Hardcover. 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. This text gives special emphasis to problems with non-unique lower level optimal solutions. Both 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. 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). Shipping may be from our Sydney, NSW warehouse or from our UK or US warehouse, depending on stock availability. Codice articolo 9781402006319

Riassunto:

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.

Contenuti: 1. Introduction. 2. Applications. 3. Linear Bilevel Problems. 4. Parametric optimization. 5. Optimality Conditions. 6. Solution Algorithms. 7. Non-unique Lower Level Solution. 8. Discrete Bilevel Problems. References. Notations. Index.

Dati bibliografici

Titolo: Foundations of Bilevel Programming (...
Casa editrice: Kluwer Academic Publishers, New York, NY
Data di pubblicazione: 2002
Legatura: Hardcover
Condizione: new