IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v93y1997i3d10.1023_a1022695113803.html
   My bibliography  Save this article

Stability of Regularized Bilevel Programming Problems

Author

Listed:
  • M. B. Lignola

    (Università di Napoli “Federico II,”)

  • J. Morgan

    (Università di Napoli “Federico II,”)

Abstract

A bilevel programming problem S is considered. First, sufficient conditions of minimal character are given on the data of the problem in order to guarantee the lower semicontinuity of the marginal function of the upper level problem. Then, for ε>0, a regularized problem S(ε) is considered for which continuity of the regularized marginal function and convergence of the approximate value, as ε goes to zero, are obtained. Moreover, under perturbations on the data, convergence results for the perturbed marginal functions and the solutions to the problem S n(ε) are given for any ε>0.

Suggested Citation

  • M. B. Lignola & J. Morgan, 1997. "Stability of Regularized Bilevel Programming Problems," Journal of Optimization Theory and Applications, Springer, vol. 93(3), pages 575-596, June.
    • Handle: RePEc:spr:joptap:v:93:y:1997:i:3:d:10.1023_a:1022695113803
    DOI: 10.1023/A:1022695113803
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1023/A:1022695113803
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1023/A:1022695113803?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. H. Bonnel & J. Morgan, 2006. "Semivectorial Bilevel Optimization Problem: Penalty Approach," Journal of Optimization Theory and Applications, Springer, vol. 131(3), pages 365-382, December.
    2. Francesco Caruso & Maria Carmela Ceparano & Jacqueline Morgan, 2019. "Subgame Perfect Nash Equilibrium: A Learning Approach via Costs to Move," Dynamic Games and Applications, Springer, vol. 9(2), pages 416-432, June.
    3. Henri Bonnel & Léonard Todjihoundé & Constantin Udrişte, 2015. "Semivectorial Bilevel Optimization on Riemannian Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 167(2), pages 464-486, November.
    4. Ming Hu & Masao Fukushima, 2011. "Variational Inequality Formulation of a Class of Multi-Leader-Follower Games," Journal of Optimization Theory and Applications, Springer, vol. 151(3), pages 455-473, December.
    5. Francesco Caruso & Maria Carmela Ceparano & Jacqueline Morgan, 2022. "Asymptotic Behavior of Subgame Perfect Nash Equilibria in Stackelberg Games," CSEF Working Papers 661, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy.
    6. L. Mallozi & S. Tijs & M. Voorneveld, 2000. "Infinite Hierarchical Potential Games," Journal of Optimization Theory and Applications, Springer, vol. 107(2), pages 287-296, November.
    7. Gaoxi Li & Xinmin Yang, 2021. "Convexification Method for Bilevel Programs with a Nonconvex Follower’s Problem," Journal of Optimization Theory and Applications, Springer, vol. 188(3), pages 724-743, March.
    8. Abdelmalek Aboussoror & Samir Adly, 2018. "New necessary and sufficient optimality conditions for strong bilevel programming problems," Journal of Global Optimization, Springer, vol. 70(2), pages 309-327, February.
    9. M. Lignola & Jacqueline Morgan, 2012. "Approximate values for mathematical programs with variational inequality constraints," Computational Optimization and Applications, Springer, vol. 53(2), pages 485-503, October.
    10. Gaoxi Li & Zhongping Wan, 2018. "On Bilevel Programs with a Convex Lower-Level Problem Violating Slater’s Constraint Qualification," Journal of Optimization Theory and Applications, Springer, vol. 179(3), pages 820-837, December.
    11. M. B. Lignola & J. Morgan, 2007. "On Convergence Results for Weak Efficiency in Vector Optimization Problems with Equilibrium Constraints," Journal of Optimization Theory and Applications, Springer, vol. 133(1), pages 117-121, April.
    12. M. Beatrice Lignola & Jacqueline Morgan, 2012. "Approximating Security Values of MinSup Problems with Quasi-variational Inequality Constraints," CSEF Working Papers 321, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy, revised 09 Oct 2014.
    13. Lorenzo Lampariello & Simone Sagratella, 2020. "Numerically tractable optimistic bilevel problems," Computational Optimization and Applications, Springer, vol. 76(2), pages 277-303, June.
    14. M. Beatrice Lignola & Jacqueline Morgan, 2013. "Asymptotic Behavior of Regularized OptimizationProblems with Quasi-variational Inequality Constraints," CSEF Working Papers 350, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:joptap:v:93:y:1997:i:3:d:10.1023_a:1022695113803. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.