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

  • Vyacheslav V. Kalashnikov
  • Stephan Dempe
  • Gerardo A. Pérez-Valdés
  • Nataliya I. Kalashnykova
Part of the Smart Innovation, Systems and Technologies book series (SIST, volume 10)


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.


Nash Equilibrium Level Problem Bilevel Programming Lower Level Problem Bilevel Programming Problem 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Vyacheslav V. Kalashnikov
    • 1
  • Stephan Dempe
    • 2
  • Gerardo A. Pérez-Valdés
    • 3
  • Nataliya I. Kalashnykova
    • 4
  1. 1.ITESMMonterreyMexico
  2. 2.TU Bergacademie FreibergFreibergGermany
  3. 3.NTNUTrondheimNorway
  4. 4.UANLSan Nicolás de los GarzaMexico

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