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A Fenchel–Lagrange Duality Approach for a Bilevel Programming Problem with Extremal-Value Function

Author

Listed:
  • Abdelmalek Aboussoror

    (Université Cadi Ayyad)

  • Samir Adly

    (Université de Limoges)

Abstract

In this paper, for a bilevel programming problem (S) with an extremal-value function, we first give its Fenchel–Lagrange dual problem. Under appropriate assumptions, we show that a strong duality holds between them. Then, we provide optimality conditions for (S) and its dual. Finally, we show that the resolution of the dual problem is equivalent to the resolution of a one-level convex minimization problem.

Suggested Citation

  • Abdelmalek Aboussoror & Samir Adly, 2011. "A Fenchel–Lagrange Duality Approach for a Bilevel Programming Problem with Extremal-Value Function," Journal of Optimization Theory and Applications, Springer, vol. 149(2), pages 254-268, May.
    • Handle: RePEc:spr:joptap:v:149:y:2011:i:2:d:10.1007_s10957-011-9831-5
    DOI: 10.1007/s10957-011-9831-5
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    References listed on IDEAS

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    1. Gert Wanka & Radu Boţ & Emese Vargyas, 2007. "On the relations between different duals assigned to composed optimization problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 66(1), pages 47-68, August.
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    Cited by:

    1. M. D. Fajardo & J. Vidal, 2018. "Necessary and Sufficient Conditions for Strong Fenchel–Lagrange Duality via a Coupling Conjugation Scheme," Journal of Optimization Theory and Applications, Springer, vol. 176(1), pages 57-73, January.

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