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Reduction of Dimension of the Upper Level Problem in a Bilevel Programming Model Part 2

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Intelligent Decision Technologies

Part of the book series: Smart Innovation, Systems and Technologies ((SIST,volume 10))

Abstract

The paper deals with a problem of reducing dimension of the upper level problem in a bilevel programming model. In order to diminish the number of variables governed by the leader at the upper level, we create the second follower supplied with the objective function coinciding with that of the leader and pass part of the uppser level variables to the lower level to be governed but the second follower. The lower level problem is also modified and becomes a Nash equilibrium problem solved by the original and the new followers. We look for conditions that guarantee that the modified and the original bilevel programming problems share at least one optimal solution.

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References

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Author information

Authors and Affiliations

  1. ITESM, Campus Monterrey, Monterrey, Mexico

    Vyacheslav V. Kalashnikov

  2. TU Bergacademie Freiberg, Freiberg, Germany

    Stephan Dempe

  3. NTNU, Trondheim, Norway

    Gerardo A. Pérez-Valdés

  4. UANL, San Nicolás de los Garza, Mexico

    Nataliya I. Kalashnykova

Authors
  1. Vyacheslav V. Kalashnikov
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  2. Stephan Dempe
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  3. Gerardo A. Pérez-Valdés
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  4. Nataliya I. Kalashnykova
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Editor information

Editors and Affiliations

  1. Graduate School of Information, Production and Systems (IPS), Waseda University, 2-7 Hibikino Wakamatsuku, 808-0135, Fukuoka, Kitakyushu, Japan

    Junzo Watada

  2. Sellinger School of Business and Management, Loyola University Maryland, 4501 N Charles Street, 21210, Baltimore, MD, USA

    Gloria Phillips-Wren

  3. School of Electrical and Information Engineering, University of South Australia, Mawson Lakes Campus Adelaide, 5095, South Australia, SA, Australia

    Lakhmi C. Jain

  4. KES International, Shoreham-by-seaWest Sussex, PO Box 2115, BN43 9AF, United Kingdom

    Robert J. Howlett

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© 2011 Springer-Verlag Berlin Heidelberg

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Kalashnikov, V.V., Dempe, S., Pérez-Valdés, G.A., Kalashnykova, N.I. (2011). Reduction of Dimension of the Upper Level Problem in a Bilevel Programming Model Part 2. In: Watada, J., Phillips-Wren, G., Jain, L.C., Howlett, R.J. (eds) Intelligent Decision Technologies. Smart Innovation, Systems and Technologies, vol 10. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22194-1_27

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  • DOI: https://doi.org/10.1007/978-3-642-22194-1_27

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-22193-4

  • Online ISBN: 978-3-642-22194-1

  • eBook Packages: EngineeringEngineering (R0)

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