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New Constraint Qualifications for S-Stationarity for MPEC with Nonsmooth Objective

Author

Listed:
  • Peng Zhang

    (School of Management, Shanghai University, Shanghai 200444, P. R. China)

  • Jin Zhang

    (Department of Mathematics, Southern University of Science and Technology, Shenzhen, P. R. China)

  • Gui-Hua Lin

    (School of Management, Shanghai University, Shanghai 200444, P. R. China)

  • Xinmin Yang

    (College of Mathematics Science, Chongqing Normal University, Chongqing 401131, P. R. China)

Abstract

This paper considers a mathematical problem with equilibrium constraints (MPEC) in which the objective is locally Lipschitz continuous but not continuously differentiable everywhere. Our focus is on constraint qualifications for the nonsmooth S-stationarity in the sense of the limiting subdifferentials. First, although the MPEC-LICQ is not a constraint qualification for the nonsmooth S-stationarity, we show that the MPEC-LICQ can serve as a constraint qualification for the nonsmooth S-stationarity under some kind of regularity. Then, we extend some new constraint qualifications for nonlinear programs to the considered nonsmooth MPEC and show that all of them can serve as constraint qualifications for the nonsmooth S-stationarity. We further extend these results to the multiobjective case.

Suggested Citation

  • Peng Zhang & Jin Zhang & Gui-Hua Lin & Xinmin Yang, 2019. "New Constraint Qualifications for S-Stationarity for MPEC with Nonsmooth Objective," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 36(02), pages 1-16, April.
    • Handle: RePEc:wsi:apjorx:v:36:y:2019:i:02:n:s0217595919400013
    DOI: 10.1142/S0217595919400013
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    References listed on IDEAS

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    1. Lei Guo & Gui-Hua Lin, 2013. "Notes on Some Constraint Qualifications for Mathematical Programs with Equilibrium Constraints," Journal of Optimization Theory and Applications, Springer, vol. 156(3), pages 600-616, March.
    2. Jane J. Ye & Jin Zhang, 2014. "Enhanced Karush–Kuhn–Tucker Conditions for Mathematical Programs with Equilibrium Constraints," Journal of Optimization Theory and Applications, Springer, vol. 163(3), pages 777-794, December.
    3. Jane J. Ye, 2011. "Necessary Optimality Conditions for Multiobjective Bilevel Programs," Mathematics of Operations Research, INFORMS, vol. 36(1), pages 165-184, February.
    4. Lei Guo & Gui-Hua Lin & Jane J. Ye, 2013. "Second-Order Optimality Conditions for Mathematical Programs with Equilibrium Constraints," Journal of Optimization Theory and Applications, Springer, vol. 158(1), pages 33-64, July.
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    Cited by:

    1. Shisen Liu & Xiaojun Chen, 2023. "Lifted stationary points of sparse optimization with complementarity constraints," Computational Optimization and Applications, Springer, vol. 84(3), pages 973-1003, April.

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