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Field name	Details
Dewey Class	515.64
Title	Foundations of Bilevel Programming ([EBook] /) / by Stephan Dempe.
Author	Dempe, Stephan
Other name(s)	SpringerLink (Online service)
Publication	Boston, MA : : Springer US, , 2002.
Physical Details	VIII, 309 p. : online resource.
Series	Nonconvex Optimization and Its Applications 1571-568X ; ; 61
ISBN	9780306480454
Summary Note	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.:
Contents note	Applications -- Linear Bilevel Problems -- Parametric Optimization -- Optimality Conditions -- Solution Algorithms -- Nonunique Lower Level Solution -- Discrete Bilevel Problems.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/b101970
Links to Related Works	Subject References: Calculus of variations . Calculus of variations and optimal control; optimization . Decision making . Mathematical optimization . Mathematics . Operation Research/Decision Theory . Operations research . Optimization . Authors: Dempe, Stephan . Corporate Authors: SpringerLink (Online service) . Series: Nonconvex Optimization and Its Applications . Classification: 515.64 .

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Foundations of Bilevel Programming

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