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On Approximate Stationary Points of the Regularized Mathematical Program with Complementarity Constraints

Author

Listed:
  • Jean-Pierre Dussault

    (Université de Sherbrooke)

  • Mounir Haddou

    (Univ Rennes, INSA Rennes, CNRS, IRMAR - UMR 6625)

  • Abdeslam Kadrani

    (INSEA, Laboratoire SI2M Rabat-Instituts)

  • Tangi Migot

    (University of Guelph)

Abstract

We discuss the convergence of regularization methods for mathematical programs with complementarity constraints with approximate sequence of stationary points. It is now well accepted in the literature that, under some tailored constraint qualification, the genuine necessary optimality condition for this problem is the M-stationarity condition. It has been pointed out, (Kanzow and Schwartz in Math Oper Res 40(2):253–275. 2015), that relaxation methods with approximate stationary points fail to ensure convergence to M-stationary points. We define a new strong approximate stationarity concept, and we prove that a sequence of strong approximate stationary points always converges to an M-stationary solution. We also prove under weak assumptions the existence of strong approximate stationary points in the neighborhood of an M-stationary solution.

Suggested Citation

  • Jean-Pierre Dussault & Mounir Haddou & Abdeslam Kadrani & Tangi Migot, 2020. "On Approximate Stationary Points of the Regularized Mathematical Program with Complementarity Constraints," Journal of Optimization Theory and Applications, Springer, vol. 186(2), pages 504-522, August.
    • Handle: RePEc:spr:joptap:v:186:y:2020:i:2:d:10.1007_s10957-020-01706-w
    DOI: 10.1007/s10957-020-01706-w
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    References listed on IDEAS

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    5. Michael L. Flegel & Christian Kanzow, 2006. "A direct proof for M-stationarity under MPEC-GCQ for mathematical programs with equilibrium constraints," Springer Optimization and Its Applications, in: Stephan Dempe & Vyacheslav Kalashnikov (ed.), Optimization with Multivalued Mappings, pages 111-122, Springer.
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