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A quadratic objective penalty function for bilevel programming

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Abstract

The bilevel programming is applied to solve hierarchical intelligence control problems in such fields as industry, agriculture, transportation, military, and so on. This paper presents a quadratic objective penalty function with two penalty parameters for inequality constrained bilevel programming. Under some conditions, the optimal solution to the bilevel programming defined by the quadratic objective penalty function is proved to be an optimal solution to the original bilevel programming. Moreover, based on the quadratic objective penalty function, an algorithm is developed to find an optimal solution to the original bilevel programming, and its convergence proved under some conditions. Furthermore, under the assumption of convexity at lower level problems, a quadratic objective penalty function without lower level problems is defined and is proved equal to the original bilevel programming.

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Authors and Affiliations

  1. College of Business and Administration, Zhejiang University of Technology, Hangzhou, 310023, China

    Min Jiang, Zhiqing Meng, Rui Shen & Xinsheng Xu

Authors
  1. Min Jiang
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  2. Zhiqing Meng
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  3. Rui Shen
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  4. Xinsheng Xu
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Corresponding author

Correspondence to Min Jiang.

Additional information

This research was supported by the National Natural Science Foundation of China under Grant Nos. 11271329 and 10971193.

This paper was recommended for publication by Editor DAI Yuhong.

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Jiang, M., Meng, Z., Shen, R. et al. A quadratic objective penalty function for bilevel programming. J Syst Sci Complex 27, 327–337 (2014). https://doi.org/10.1007/s11424-014-2128-7

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  • DOI: https://doi.org/10.1007/s11424-014-2128-7

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