J. Oper. Res. Soc. China https://doi.org/10.1007/s40305-018-0205-7 An Objective Penalty Method for Optimistic Bilevel Programming Problems 1 2 3 June Liu · Tao Zhang · Yu-Xin Fan · 1 1 Bing Han · Yue Zheng Received: 2 April 2017 / Revised: 25 February 2018 / Accepted: 9 May 2018 © Operations Research Society of China, Periodicals Agency of Shanghai University, Science Press, and Springer-Verlag GmbH Germany, part of Springer Nature 2018 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. Keywords Bilevel programming · Optimistic formulation · Penalty method · Objective penalty method Mathematics Subject Classiﬁcation 90C26 · 90C30 This work was supported by the National Natural Science Foundation of China (Nos. 11501233 and 61673006) and the Natural Science Research Project of Universities of Anhui Province (No. KJ2016B025). Tao Zhang email@example.com June Liu firstname.lastname@example.org Yu-Xin Fan email@example.com Bing Han firstname.lastname@example.org Yue Zheng email@example.com School of Management, Huaibei Normal University, Huaibei
Journal of the Operations Research Society of China – Springer Journals
Published: Jun 1, 2018
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