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An Objective Penalty Function of Bilevel Programming

Author

Listed:
  • Zhiqing Meng

    (Zhejiang University of Technology)

  • Chuangyin Dang

    (City University of Hong Kong)

  • Rui Shen

    (Zhejiang University of Technology)

  • Ming Jiang

    (Zhejiang University of Technology)

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.

Suggested Citation

  • Zhiqing Meng & Chuangyin Dang & Rui Shen & Ming Jiang, 2012. "An Objective Penalty Function of Bilevel Programming," Journal of Optimization Theory and Applications, Springer, vol. 153(2), pages 377-387, May.
    • Handle: RePEc:spr:joptap:v:153:y:2012:i:2:d:10.1007_s10957-011-9945-9
    DOI: 10.1007/s10957-011-9945-9
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    References listed on IDEAS

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    1. G. S. Liu & J. Y. Han & J. Z. Zhang, 2001. "Exact Penalty Functions for Convex Bilevel Programming Problems," Journal of Optimization Theory and Applications, Springer, vol. 110(3), pages 621-643, September.
    2. Ankhili, Z. & Mansouri, A., 2009. "An exact penalty on bilevel programs with linear vector optimization lower level," European Journal of Operational Research, Elsevier, vol. 197(1), pages 36-41, August.
    3. Yang, Hai & Zhang, Xiaoning & Meng, Qiang, 2007. "Stackelberg games and multiple equilibrium behaviors on networks," Transportation Research Part B: Methodological, Elsevier, vol. 41(8), pages 841-861, October.
    4. Kogan, Konstantin & Tapiero, Charles S., 2009. "Optimal co-investment in supply chain infrastructure," European Journal of Operational Research, Elsevier, vol. 192(1), pages 265-276, January.
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