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Improved Convergence Properties of the Relaxation Schemes of Kadrani et al. and Kanzow and Schwartz for MPEC

Author

Listed:
  • Na Xu

    (School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, P. R. China)

  • Xide Zhu

    (Faculty of Business Administration, Yokohama National University, Yokohama 240-8501, Japan)

  • Li-Ping Pang

    (School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, P. R. China)

  • Jian Lv

    (School of Finance, Zhejiang University of Finance and Economics, Hangzhou 310018, P. R. China)

Abstract

This paper concentrates on improving the convergence properties of the relaxation schemes introduced by Kadrani et al. and Kanzow and Schwartz for mathematical program with equilibrium constraints (MPEC) by weakening the original constraint qualifications. It has been known that MPEC relaxed constant positive-linear dependence (MPEC-RCPLD) is a class of extremely weak constraint qualifications for MPEC, which can be strictly implied by MPEC relaxed constant rank constraint qualification (MPEC-RCRCQ) and MPEC relaxed constant positive-linear dependence (MPEC-rCPLD), of course also by the MPEC constant positive-linear dependence (MPEC-CPLD). We show that any accumulation point of stationary points of these two approximation problems is M-stationarity under the MPEC-RCPLD constraint qualification, and further show that the accumulation point can even be S-stationarity coupled with the asymptotically weak nondegeneracy condition.

Suggested Citation

  • Na Xu & Xide Zhu & Li-Ping Pang & Jian Lv, 2018. "Improved Convergence Properties of the Relaxation Schemes of Kadrani et al. and Kanzow and Schwartz for MPEC," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 35(01), pages 1-20, February.
    • Handle: RePEc:wsi:apjorx:v:35:y:2018:i:01:n:s0217595918500082
    DOI: 10.1142/S0217595918500082
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    References listed on IDEAS

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    1. Nguyen Huy Chieu & Gue Myung Lee, 2013. "A Relaxed Constant Positive Linear Dependence Constraint Qualification for Mathematical Programs with Equilibrium Constraints," Journal of Optimization Theory and Applications, Springer, vol. 158(1), pages 11-32, July.
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