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Bilevel programming with convex lower level problems

In: Optimization with Multivalued Mappings

Author

Listed:
  • Joydeep Dutta

    (Indian Institute of Technology)

  • Stephan Dempe

    (Technical University Bergakademie Freiberg)

Abstract

Summary In this article we develop certain necessary optimality condition for bilevel programming problems with convex lower-level problem. The results are abstract in nature and depend on an important construction in nonsmooth analysis called the coderivative of a set-valued map.

Suggested Citation

  • Joydeep Dutta & Stephan Dempe, 2006. "Bilevel programming with convex lower level problems," Springer Optimization and Its Applications, in: Stephan Dempe & Vyacheslav Kalashnikov (ed.), Optimization with Multivalued Mappings, pages 51-71, Springer.
    • Handle: RePEc:spr:spochp:978-0-387-34221-4_3
    DOI: 10.1007/0-387-34221-4_3
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    Citations

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    Cited by:

    1. Stephan Dempe & Maria Pilecka, 2015. "Necessary optimality conditions for optimistic bilevel programming problems using set-valued programming," Journal of Global Optimization, Springer, vol. 61(4), pages 769-788, April.
    2. Guillaume Allaire Pouliot & Zhen Xie, 2022. "Degrees of Freedom and Information Criteria for the Synthetic Control Method," Papers 2207.02943, arXiv.org.
    3. Boris S. Mordukhovich & Nguyen Mau Nam & Hung M. Phan, 2012. "Variational Analysis of Marginal Functions with Applications to Bilevel Programming," Journal of Optimization Theory and Applications, Springer, vol. 152(3), pages 557-586, March.
    4. Stephan Dempe & Alain B. Zemkoho, 2011. "The Generalized Mangasarian-Fromowitz Constraint Qualification and Optimality Conditions for Bilevel Programs," Journal of Optimization Theory and Applications, Springer, vol. 148(1), pages 46-68, January.

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