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 firstname.lastname@example.org June Liu email@example.com Yu-Xin Fan firstname.lastname@example.org Bing Han email@example.com Yue Zheng firstname.lastname@example.org School of Management, Huaibei Normal University, Huaibei
Journal of the Operations Research Society of China – Springer Journals
Published: Jun 1, 2018
It’s your single place to instantly
discover and read the research
that matters to you.
Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.
All for just $49/month
Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly
Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.
Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.
Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.
All the latest content is available, no embargo periods.
“Hi guys, I cannot tell you how much I love this resource. Incredible. I really believe you've hit the nail on the head with this site in regards to solving the research-purchase issue.”Daniel C.
“Whoa! It’s like Spotify but for academic articles.”@Phil_Robichaud
“I must say, @deepdyve is a fabulous solution to the independent researcher's problem of #access to #information.”@deepthiw
“My last article couldn't be possible without the platform @deepdyve that makes journal papers cheaper.”@JoseServera