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

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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.

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Acknowledgements

This research was partially supported by a grant from “l’Ecole des Docteurs de l’UBL” and “le Conseil Régional de Bretagne”. This research was partially supported by NSERC and FRQNT grants.

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Authors and Affiliations

  1. Département d’informatique, Université de Sherbrooke, Sherbrooke, Canada

    Jean-Pierre Dussault

  2. Univ Rennes, INSA Rennes, CNRS, IRMAR - UMR 6625, 35000, Rennes, France

    Mounir Haddou

  3. INSEA, Laboratoire SI2M Rabat-Instituts, Rabat, Morocco

    Abdeslam Kadrani

  4. Department of Mathematics and Statistics, University of Guelph, Guelph, Canada

    Tangi Migot

Authors
  1. Jean-Pierre Dussault
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  2. Mounir Haddou
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  3. Abdeslam Kadrani
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  4. Tangi Migot
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Corresponding author

Correspondence to Tangi Migot.

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Communicated by Fabiàn Flores-Bazàn.

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Dussault, JP., Haddou, M., Kadrani, A. et al. On Approximate Stationary Points of the Regularized Mathematical Program with Complementarity Constraints. J Optim Theory Appl 186, 504–522 (2020). https://doi.org/10.1007/s10957-020-01706-w

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  • DOI: https://doi.org/10.1007/s10957-020-01706-w

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