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An Objective Penalty Method for Optimistic Bilevel Programming Problems

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Abstract

In this paper, we consider an optimistic nonlinear bilevel programming problem. Under some conditions, we first show that the sequence of solutions to penalty problems converges to the optimal solution of the original bilevel programming problem. We then present an objective penalty method to solve such a problem. Finally, some numerical experiments are performed to illustrate its feasibility.

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Acknowledgements

The authors thank anonymous referees for their valuable comments and suggestions, which help to improve the manuscript.

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Authors and Affiliations

  1. School of Management, Huaibei Normal University, Huaibei, 235000, Anhui, China

    June Liu, Bing Han & Yue Zheng

  2. School of Information and Mathematics, Yangtze University, Jingzhou, 434023, Hubei, China

    Tao Zhang

  3. Huazhong University of Science and Technology, Wuhan, 430074, China

    Yu-Xin Fan

Authors
  1. June Liu
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  2. Tao Zhang
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  3. Yu-Xin Fan
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  4. Bing Han
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  5. Yue Zheng
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Corresponding author

Correspondence to Tao Zhang.

Additional information

This work was supported by the National Natural Science Foundation of China (Nos. 11501233 and 61673006) and the Natural Science Research Project of Universities of Anhui Province (No. KJ2016B025).

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Liu, J., Zhang, T., Fan, YX. et al. An Objective Penalty Method for Optimistic Bilevel Programming Problems. J. Oper. Res. Soc. China 8, 177–187 (2020). https://doi.org/10.1007/s40305-018-0205-7

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  • DOI: https://doi.org/10.1007/s40305-018-0205-7

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