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It is a matter of hierarchy: a Nash equilibrium problem perspective on bilevel programming

Author

Listed:
  • Lorenzo Lampariello

    (Department of Methods and Models for Economics, Territory and Finance, University of Rome "La Sapienza")

  • Simone Sagratella

    (Department of Computer, Control and Management Engineering, University of Rome "La Sapienza")

Abstract

Inspired by the optimal value approach, we propose a new reformulation of the optimistic Bilevel programming Problem (BP) as a suitable Generalized Nash Equilibrium Problem (GNEP). We provide a complete analysis of the relationship between the original hierarchical BP and the corresponding "more democratic" GNEP. Moreover, we investigate solvability and convexity issues of our reformulation. Finally, relying on the vast literature on solution methods for GNEPs, we devise a new effective algorithmic framework for the solution of signicant classes of BPs.

Suggested Citation

  • Lorenzo Lampariello & Simone Sagratella, 2015. "It is a matter of hierarchy: a Nash equilibrium problem perspective on bilevel programming," DIAG Technical Reports 2015-07, Department of Computer, Control and Management Engineering, Universita' degli Studi di Roma "La Sapienza".
    • Handle: RePEc:aeg:report:2015-07
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    References listed on IDEAS

    as
    1. Francisco Facchinei & Lorenzo Lampariello, 2011. "Partial penalization for the solution of generalized Nash equilibrium problems," Journal of Global Optimization, Springer, vol. 50(1), pages 39-57, May.
    2. 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.
    3. Francisco Facchinei & Christian Kanzow, 2010. "Generalized Nash Equilibrium Problems," Annals of Operations Research, Springer, vol. 175(1), pages 177-211, March.
    4. Benoît Colson & Patrice Marcotte & Gilles Savard, 2007. "An overview of bilevel optimization," Annals of Operations Research, Springer, vol. 153(1), pages 235-256, September.
    5. 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.
    6. Jonathan F. Bard, 1983. "An Algorithm for Solving the General Bilevel Programming Problem," Mathematics of Operations Research, INFORMS, vol. 8(2), pages 260-272, May.
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    Cited by:

    1. Lorenzo Lampariello & Simone Sagratella, 2017. "A Bridge Between Bilevel Programs and Nash Games," Journal of Optimization Theory and Applications, Springer, vol. 174(2), pages 613-635, August.

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    More about this item

    Keywords

    Bilevel programming ; Generalized Nash Equilibrium Problems (GNEP); parametric optimization ; numerical approaches;
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