An Objective Penalty Method for Optimistic Bilevel Programming Problems

An Objective Penalty Method for Optimistic Bilevel Programming Problems 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 zt_math981@126.com June Liu xun4025@126.com Yu-Xin Fan fann.song@yahoo.com Bing Han 1668177516@qq.com Yue Zheng zhengyuestone@126.com School of Management, Huaibei Normal University, Huaibei http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of the Operations Research Society of China Springer Journals

An Objective Penalty Method for Optimistic Bilevel Programming Problems

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Publisher
Operations Research Society of China
Copyright
Copyright © 2018 by Operations Research Society of China, Periodicals Agency of Shanghai University, Science Press, and Springer-Verlag GmbH Germany, part of Springer Nature
Subject
Mathematics; Operations Research, Management Science
ISSN
2194-668X
eISSN
2194-6698
D.O.I.
10.1007/s40305-018-0205-7
Publisher site
See Article on Publisher Site

Abstract

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 zt_math981@126.com June Liu xun4025@126.com Yu-Xin Fan fann.song@yahoo.com Bing Han 1668177516@qq.com Yue Zheng zhengyuestone@126.com School of Management, Huaibei Normal University, Huaibei

Journal

Journal of the Operations Research Society of China – Springer Journals

Published: Jun 1, 2018

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