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New partial cooperation model for bilevel programming problems |
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| Authors: | Shihui Jia Zhongping Wan Yuqiang Feng Guangmin Wang |
| Affiliation: | 1. School of Mathematics and Statistic, Wuhan University, Wuhan 430072, P. R. China;Hubei Province Key Laboratory of Systems Science in Metallurgical Process, Wuhan University of Science and Technology, Wuhan 430081, P. R. China;Mathematics Department, College of Sciences, Wuhan University of Science and Technology, Wuhan 430081, P. R. China 2. School of Mathematics and Statistic, Wuhan University, Wuhan 430072, P. R. China 3. Hubei Province Key Laboratory of Systems Science in Metallurgical Process, Wuhan University of Science and Technology, Wuhan 430081, P. R. China |
| Abstract: | Partial cooperation models are studied for many years to solve the bilevel programming problems where the follower's optimal reaction is not unique. However, in these existed models, the follower's cooperation level does not depend on the leader's decision. A new model is proposed to solve this deficiency. It is proved the feasibility of the new model when the reaction set of the lower level is lower semi-continuous. And the numerical results show that the new model has optimal solutions when the reaction set of the lower level is discrete, lower semi-continuous and nonlower semi-continuous. |
| Keywords: | bilevel programming reaction set optimistic model pessimistic model partial cooperation model cooperation level |
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