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Exact Penalty Functions for Convex Bilevel Programming Problems

Author

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  • G. S. Liu
  • J. Y. Han
  • J. Z. Zhang

Abstract

In this paper, we propose a new constraint qualification for convex bilevel programming problems. Under this constraint qualification, a locally and globally exact penalty function of order 1 for a single-level reformulation of convex bilevel programming problems is given without requiring the linear independence condition and the strict complementarity condition to hold in the lower-level problem. Based on these results, locally and globally exact penalty functions for two other single-level reformulations of convex bilevel programming problems can be obtained. Furthermore, sufficient conditions for partial calmness to hold in some single-level reformulations of convex bilevel programming problems can be given.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:110:y:2001:i:3:d:10.1023_a:1017592429235
    DOI: 10.1023/A:1017592429235
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    Cited by:

    1. 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.
    2. Changrong Liu & Hanqing Wang & Zhiqiang Liu & Zhiyong Wang & Sheng Yang, 2021. "Research on a Bi-Level Collaborative Optimization Method for Planning and Operation of Multi-Energy Complementary Systems," Energies, MDPI, vol. 14(23), pages 1-20, November.
    3. Marina Prechtel & Günter Leugering & Paul Steinmann & Michael Stingl, 2012. "Optimal Design of Brittle Composite Materials: a Nonsmooth Approach," Journal of Optimization Theory and Applications, Springer, vol. 155(3), pages 962-985, December.

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