Journal of the Operations Research Society of China ›› 2020, Vol. 8 ›› Issue (1): 177-187.doi: 10.1007/s40305-018-0205-7

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An Objective Penalty Method for Optimistic Bilevel Programming Problems

June Liu1, Tao Zhang2, Yu-Xin Fan3, Bing Han1, Yue Zheng1   

  1. 1 School of Management, Huaibei Normal University, Huaibei 235000, Anhui, China;
    2 School of Information and Mathematics, Yangtze University, Jingzhou 434023, Hubei, China;
    3 Huazhong University of Science and Technology, Wuhan 430074, China
  • Received:2017-04-02 Revised:2018-02-25 Online:2020-03-30 Published:2020-02-18
  • Contact: Tao Zhang, June Liu, Yu-Xin Fan, Bing Han, Yue Zheng E-mail:zt_math981@126.com;xun4025@126.com;fann.song@yahoo.com;1668177516@qq.com;zhengyuestone@126.com

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.

Key words: Bilevel programming, Optimistic formulation, Penalty method, Objective penalty method

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