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Smoothing partial exact penalty splitting method for mathematical programs with equilibrium constraints

Author

Listed:
  • Suhong Jiang

    (Nanjing University)

  • Jin Zhang

    (Hong Kong Baptist University)

  • Caihua Chen

    (Nanjing University)

  • Guihua Lin

    (Shanghai University)

Abstract

Mathematical program with equilibrium constraints (MPEC) is an important problem in mathematical programming as it arises frequently in a broad spectrum of fields. In this paper, we propose an implementable smoothing partial exact penalty method to solve MPEC, where the subproblems are solved inexactly by the proximal alternating linearized minimization method. Under the extend MPEC-NNAMCQ, the proposed method is shown to be convergent to an M-stationary point of the MPEC.

Suggested Citation

  • Suhong Jiang & Jin Zhang & Caihua Chen & Guihua Lin, 2018. "Smoothing partial exact penalty splitting method for mathematical programs with equilibrium constraints," Journal of Global Optimization, Springer, vol. 70(1), pages 223-236, January.
    • Handle: RePEc:spr:jglopt:v:70:y:2018:i:1:d:10.1007_s10898-017-0539-4
    DOI: 10.1007/s10898-017-0539-4
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    References listed on IDEAS

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    1. Holger Scheel & Stefan Scholtes, 2000. "Mathematical Programs with Complementarity Constraints: Stationarity, Optimality, and Sensitivity," Mathematics of Operations Research, INFORMS, vol. 25(1), pages 1-22, February.
    2. J. J. Ye & X. Y. Ye, 1997. "Necessary Optimality Conditions for Optimization Problems with Variational Inequality Constraints," Mathematics of Operations Research, INFORMS, vol. 22(4), pages 977-997, November.
    3. Gui-Hua Lin & Masao Fukushima, 2005. "A Modified Relaxation Scheme for Mathematical Programs with Complementarity Constraints," Annals of Operations Research, Springer, vol. 133(1), pages 63-84, January.
    4. X. M. Hu & D. Ralph, 2004. "Convergence of a Penalty Method for Mathematical Programming with Complementarity Constraints," Journal of Optimization Theory and Applications, Springer, vol. 123(2), pages 365-390, November.
    5. G. H. Lin & M. Fukushima, 2006. "Hybrid Approach with Active Set Identification for Mathematical Programs with Complementarity Constraints," Journal of Optimization Theory and Applications, Springer, vol. 128(1), pages 1-28, January.
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