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Nonconvex Optimization and Its Applications

Foundations of Bilevel Programming

Authors: Dempe, Stephan

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About this book

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.

Table of contents (8 chapters)

Buy this book

eBook $229.00
price for USA (gross)
  • ISBN 978-0-306-48045-4
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $289.00
price for USA
  • ISBN 978-1-4020-0631-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $289.00
price for USA
  • ISBN 978-1-4419-5220-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Foundations of Bilevel Programming
Authors
Series Title
Nonconvex Optimization and Its Applications
Series Volume
61
Copyright
2002
Publisher
Springer US
Copyright Holder
The Editor(s) (if applicable) and The Author(s) 2018
eBook ISBN
978-0-306-48045-4
DOI
10.1007/b101970
Hardcover ISBN
978-1-4020-0631-9
Softcover ISBN
978-1-4419-5220-2
Series ISSN
1571-568X
Edition Number
1
Number of Pages
VIII, 309
Topics