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Foundations of Bilevel Programming

  • Book
  • © 2002

Overview

Authors:
  1. Stephan Dempe

    1. Freiberg University of Mining and Technology, Freiberg, Germany

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Part of the book series: Nonconvex Optimization and Its Applications (NOIA, volume 61)

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Table of contents (8 chapters)

  1. Front Matter

    Pages i-viii
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  2. Introduction

    Pages 1-6

  3. Applications

    Pages 7-20

  4. Linear Bilevel Problems

    Pages 21-60

  5. Parametric Optimization

    Pages 61-118

  6. Optimality Conditions

    Pages 119-192

  7. Solution Algorithms

    Pages 193-216

  8. Nonunique Lower Level Solution

    Pages 217-254

  9. Discrete Bilevel Problems

    Pages 255-282

  10. Back Matter

    Pages 283-309
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Keywords

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.

Authors and Affiliations

  • Freiberg University of Mining and Technology, Freiberg, Germany

    Stephan Dempe

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