Journal of Global Optimization

, Volume 39, Issue 4, pp 529–542 | Cite as

Necessary optimality conditions for bilevel set optimization problems

  • S. Dempe
  • N. Gadhi
Original Paper


Bilevel programming problems are hierarchical optimization problems where in the upper level problem a function is minimized subject to the graph of the solution set mapping of the lower level problem. In this paper necessary optimality conditions for such problems are derived using the notion of a convexificator by Luc and Jeyakumar. Convexificators are subsets of many other generalized derivatives. Hence, our optimality conditions are stronger than those using e.g., the generalized derivative due to Clarke or Michel-Penot. Using a certain regularity condition Karush-Kuhn-Tucker conditions are obtained.


Bilevel optimization Convexificator Karush-Kuhn-Tucker multipliers Necessary Optimality conditions Regularity condition Set valued mappings Support function 

Mathematics Subject Classification (2000)

Primary 49J52 90C29 Secondary 49K99 


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Copyright information

© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  1. 1.Department of Mathematics and Computers SciencesTechnical University Bergakademie FreibergFreibergGermany
  2. 2.Department of MathematicsSidi Mohamed Ben Abdellah UniversityAtlasMarokko

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