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Foundations of Bilevel Programming

Language EnglishEnglish
Book Paperback
Book Foundations of Bilevel Programming Stephan Dempe
Libristo code: 01423541
Publishers Springer-Verlag New York Inc., December 2010
Bilevel programming problems are hierarchical optimization problems where the constraints of one pro... Full description
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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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About the book

Full name Foundations of Bilevel Programming
Author Stephan Dempe
Language English
Binding Book - Paperback
Date of issue 2010
Number of pages 309
EAN 9781441952202
ISBN 1441952209
Libristo code 01423541
Publishers Springer-Verlag New York Inc.
Weight 492
Dimensions 155 x 235 x 18

Categories

Economics, Finance, Business & Management > Business & Management > Management & management techniques > Management decision making
Mathematics & Science > Mathematics > Calculus & mathematical analysis > Calculus of variations
Mathematics & Science > Mathematics > Optimization > Linear programming
Economics, Finance, Business & Management > Business & Management > Operational research
Mathematics & Science > Mathematics > Applied mathematics
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