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An Objective Penalty Function of Bilevel Programming

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Abstract

Penalty methods are very efficient in finding an optimal solution to constrained optimization problems. In this paper, we present an objective penalty function with two penalty parameters for inequality constrained bilevel programming under the convexity assumption to the lower level problem. Under some conditions, an optimal solution to a bilevel programming defined by the objective penalty function is proved to be an optimal solution to the original bilevel programming. Moreover, based on the objective penalty function, an algorithm is developed to obtain an optimal solution to the original bilevel programming, with its convergence proved under some conditions.

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Authors and Affiliations

  1. College of Business and Administration, Zhejiang University of Technology, Hangzhou, Zhejiang, 310032, China

    Zhiqing Meng, Rui Shen & Ming Jiang

  2. Department of Manufacturing Engineering & Engineering Management, City University of Hong Kong, Kowloon, Hong Kong

    Chuangyin Dang

Authors
  1. Zhiqing Meng
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  2. Chuangyin Dang
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  3. Rui Shen
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  4. Ming Jiang
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Correspondence to Zhiqing Meng.

Additional information

Communicated by Guang-ya Chen.

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Meng, Z., Dang, C., Shen, R. et al. An Objective Penalty Function of Bilevel Programming. J Optim Theory Appl 153, 377–387 (2012). https://doi.org/10.1007/s10957-011-9945-9

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  • DOI: https://doi.org/10.1007/s10957-011-9945-9

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