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140122  eng 
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a 9780306480454

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1 

a Dempe, Stephan

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0 
0 
a Foundations of Bilevel Programming
h Elektronische Ressource
c by Stephan Dempe

250 


a 1st ed. 2002

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a New York, NY
b Springer US
c 2002, 2002

300 


a VIII, 309 p
b online resource

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0 

a Applications  Linear Bilevel Problems  Parametric Optimization  Optimality Conditions  Solution Algorithms  Nonunique Lower Level Solution  Discrete Bilevel Problems

653 


a Operations research

653 


a Optimization

653 


a Calculus of Variations and Optimization

653 


a Mathematical optimization

653 


a Operations Research and Decision Theory

653 


a Calculus of variations

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0 
7 
a eng
2 ISO 6392

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b SBA
a Springer Book Archives 2004

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a Nonconvex Optimization and Its Applications

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0 
a 10.1007/b101970

856 
4 
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u https://doi.org/10.1007/b101970?nosfx=y
x Verlag
3 Volltext

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a 515.64

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a 519.6

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a Bilevel programming problems are hierarchical optimization problems where the constraints of one problem (the socalled 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 onelevel optimization problem having an implicitly defined objective function. Special emphasize in the book is on problems having nonunique 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 onelevel 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
