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Journal of Global Optimization

, Volume 68, Issue 2, pp 255–277 | Cite as

Solving discrete linear bilevel optimization problems using the optimal value reformulation

  • S. DempeEmail author
  • F. Mefo Kue
Article

Abstract

In this article, we consider two classes of discrete bilevel optimization problems which have the peculiarity that the lower level variables do not affect the upper level constraints. In the first case, the objective functions are linear and the variables are discrete at both levels, and in the second case only the lower level variables are discrete and the objective function of the lower level is linear while the one of the upper level can be nonlinear. Algorithms for computing global optimal solutions using Branch and Cut and approximation of the optimal value function of the lower level are suggested. Their convergence is shown and we illustrate each algorithm via an example.

Keywords

Bilevel programming Solution algorithm Discrete parametric optimization Global optimization 

Mathematics Subject Classification

90C11 90C10 90C29 

Notes

Acknowledgments

The authors wish to thank S. Franke and P. Mehlitz for many helpful comments and recommendations.

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Department of Mathematics and Computer ScienceTU Bergakademie FreibergFreibergGermany

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