Computational Optimization and Applications

, Volume 63, Issue 3, pp 685–703 | Cite as

On the solution of convex bilevel optimization problems

  • S. DempeEmail author
  • S. Franke


An algorithm is presented for solving bilevel optimization problems with fully convex lower level problems. Convergence to a local optimal solution is shown under certain weak assumptions. This algorithm uses the optimal value transformation of the problem. Transformation of the bilevel optimization problem using the Fritz-John necessary optimality conditions applied to the lower level problem is shown to exhibit almost the same difficulties for solving the problem as the use of the Karush–Kuhn–Tucker conditions.


Bilevel programming Mathematical programs with equilibrium constraints Optimal value transformation KKT-transformation Solution algorithm 

Mathematics Subject Classification

90C26 91A65 


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.TU Bergakademie FreibergFreibergGermany

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