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Reduction of the Dimension of the Upper Level Problem in a Bilevel Optimization Model

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Bilevel Programming Problems

Part of the book series: Energy Systems ((ENERGY))

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Abstract

Aim of this chapter is a possible reduction of the upper level problem’s dimension. This is necessary for solving the \(\mathcal {NP}\)-hard bilevel optimization problem especially in case of stochastic data. To realize this, a second follower’s problem is composed and the bilevel problem is replaced with one where a parametric Nash equilibrium between two followers is considered in the lower level. The cases of linear and nonlinear bilevel optimization are described in detail. An example is used to illustrate this idea.

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Authors and Affiliations

  1. Fak. für Mathematik und Informatik, TU Bergakademie Freiberg, Freiberg, Sachsen, Germany

    Stephan Dempe

  2. Department of Systems and Industrial Engineering, Tecnologico de Monterrey (ITESM), Campus Monterrey, Av. Eugenio Garza Sada 2501 Sur, 64849, Monterrey, NL, Mexico

    Vyacheslav Kalashnikov

  3. Department of Social Modeling, Central Economics and Mathematics Institute (CEMI), Russian Academy of Sciences, Nakhimovsky pr. 47, Moscow, 117418, Russian Federation

    Vyacheslav Kalashnikov

  4. Department of Computing, Sumy State University, Rimsky-Korsakov st. 2, Sumy, 40007, Ukraine

    Vyacheslav Kalashnikov

  5. Department of Industrial Economics, Norwegian University of Science and Technology (NTNU), Trondheim, Norway

    Gerardo A. Pérez-Valdés

  6. Facultad Ciencias Físico-Mathemáticas (FCFM), Universidad Autónoma de Nuevo León (UANL), San Nicolás de los Garza, Mexico

    Nataliya Kalashnykova

Authors
  1. Stephan Dempe
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  2. Vyacheslav Kalashnikov
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  3. Gerardo A. Pérez-Valdés
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  4. Nataliya Kalashnykova
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Corresponding author

Correspondence to Stephan Dempe .

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© 2015 Springer-Verlag Berlin Heidelberg

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Dempe, S., Kalashnikov, V., Pérez-Valdés, G.A., Kalashnykova, N. (2015). Reduction of the Dimension of the Upper Level Problem in a Bilevel Optimization Model. In: Bilevel Programming Problems. Energy Systems. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-45827-3_8

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  • DOI: https://doi.org/10.1007/978-3-662-45827-3_8

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-45826-6

  • Online ISBN: 978-3-662-45827-3

  • eBook Packages: EnergyEnergy (R0)

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