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

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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.

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Acknowledgements

The authors are grateful to three anonymous referees for their helpful comments and suggestions, which have led to much improvement of the paper.

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Authors and Affiliations

  1. School of Management and Engineering, Nanjing University, Nanjing, China

    Suhong Jiang & Caihua Chen

  2. Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, China

    Jin Zhang

  3. School of Management, Shanghai University, Shanghai, China

    Guihua Lin

Authors
  1. Suhong Jiang
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  2. Jin Zhang
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  3. Caihua Chen
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  4. Guihua Lin
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Corresponding author

Correspondence to Guihua Lin.

Additional information

This work was supported in part by NSFC (Nos. 11401300, 11431004, 11671250, 11601458) and Humanity and Social Science Foundation of Ministry of Education of China (No. 15YJA630034).

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Jiang, S., Zhang, J., Chen, C. et al. Smoothing partial exact penalty splitting method for mathematical programs with equilibrium constraints. J Glob Optim 70, 223–236 (2018). https://doi.org/10.1007/s10898-017-0539-4

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  • DOI: https://doi.org/10.1007/s10898-017-0539-4

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