
Foundations of Bilevel Programming
Stephan Dempe(Author)
Kluwer Academic Publishers
Published on 31. May 2002
Book
Hardback
VIII, 309 pages
978-1-4020-0631-9 (ISBN)
Description
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.
Audience: Applied mathematicians and economists working in optimization, operations research, and economic modelling. Students interested in optimization will also find this book useful.
More details
Series
Edition
2002 ed.
Language
English
Place of publication
New York
United States
Target group
Professional and scholarly
Research
Illustrations
VIII, 309 p.
Dimensions
Height: 241 mm
Width: 160 mm
Thickness: 22 mm
Weight
653 gr
ISBN-13
978-1-4020-0631-9 (9781402006319)
DOI
10.1007/b101970
Schweitzer Classification
Other editions
Additional editions

Stephan Dempe
Foundations of Bilevel Programming
Book
12/2010
Springer
€235.39
Shipment within 15-20 days

Stephan Dempe
Foundations of Bilevel Programming
E-Book
12/2005
Kluwer Academic/Plenum Publishers
€223.63
Available for download
Content
Applications.- Linear Bilevel Problems.- Parametric Optimization.- Optimality Conditions.- Solution Algorithms.- Nonunique Lower Level Solution.- Discrete Bilevel Problems.