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Optimality Conditions for Optimistic Bilevel Programming Problem Using Convexifactors

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  • Bhawna Kohli

    (University of Delhi)

Abstract

In this article, we introduce two versions of nonsmooth extension of Abadie constraint qualification in terms of convexifactors and Clarke subdifferential and employ the weaker one to develop new necessary Karush–Kuhn–Tucker type optimality conditions for optimistic bilevel programming problem with convex lower-level problem, using an upper estimate of Clarke subdifferential of value function in variational analysis and the concept of convexifactor.

Suggested Citation

  • Bhawna Kohli, 2012. "Optimality Conditions for Optimistic Bilevel Programming Problem Using Convexifactors," Journal of Optimization Theory and Applications, Springer, vol. 152(3), pages 632-651, March.
    • Handle: RePEc:spr:joptap:v:152:y:2012:i:3:d:10.1007_s10957-011-9941-0
    DOI: 10.1007/s10957-011-9941-0
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    References listed on IDEAS

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    1. Boris S. Mordukhovich & Nguyen Mau Nam, 2005. "Variational Stability and Marginal Functions via Generalized Differentiation," Mathematics of Operations Research, INFORMS, vol. 30(4), pages 800-816, November.
    2. J. J. Ye & X. Y. Ye, 1997. "Necessary Optimality Conditions for Optimization Problems with Variational Inequality Constraints," Mathematics of Operations Research, INFORMS, vol. 22(4), pages 977-997, November.
    3. J. Dutta & S. Chandra, 2002. "Convexifactors, Generalized Convexity, and Optimality Conditions," Journal of Optimization Theory and Applications, Springer, vol. 113(1), pages 41-64, April.
    4. X. F. Li & J. Z. Zhang, 2006. "Necessary Optimality Conditions in Terms of Convexificators in Lipschitz Optimization," Journal of Optimization Theory and Applications, Springer, vol. 131(3), pages 429-452, December.
    5. S. Dempe, 1997. "First-Order Necessary Optimality Conditions for General Bilevel Programming Problems," Journal of Optimization Theory and Applications, Springer, vol. 95(3), pages 735-739, December.
    6. Jane J. Ye, 2006. "Constraint Qualifications and KKT Conditions for Bilevel Programming Problems," Mathematics of Operations Research, INFORMS, vol. 31(4), pages 811-824, November.
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    Cited by:

    1. Nazih Abderrazzak Gadhi, 2021. "Comments on “A Note on the Paper “Optimality Conditions for Optimistic Bilevel Programming Problem Using Convexifactors””," Journal of Optimization Theory and Applications, Springer, vol. 189(3), pages 938-943, June.
    2. Do Luu, 2014. "Necessary and Sufficient Conditions for Efficiency Via Convexificators," Journal of Optimization Theory and Applications, Springer, vol. 160(2), pages 510-526, February.

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