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April  2015, 11(2): 529-547. doi: 10.3934/jimo.2015.11.529

## A new method for strong-weak linear bilevel programming problem

 1 College of Mathematics and Physics, Huanggang Normal University, Huanggang 438000, China 2 School of Mathematics and Statistics, Wuhan University, Wuhan, 430072 3 School of Science, Wuhan University of Science and Technology, Wuhan 430081, China 4 School of Economics and Management, China University of Geosciences, Wuhan 430074, China

Received  October 2012 Revised  April 2014 Published  September 2014

We first propose an exact penalty method to solve strong-weak linear bilevel programming problem (for short, SWLBP) for every fixed cooperation degree from the follower. Then, we prove that the solution of penalized problem is also that of the original problem under some conditions. Furthermore, we give some properties of the optimal value function (as a function of the follower's cooperation degree) of SWLBP. Finally, we develop a method to acquire the critical points of the optimal value function without enumerating all values of the cooperation degree from the follower, and thus this function is also achieved. Numerical results show that the proposed methods are feasible.
Citation: Yue Zheng, Zhongping Wan, Shihui Jia, Guangmin Wang. A new method for strong-weak linear bilevel programming problem. Journal of Industrial & Management Optimization, 2015, 11 (2) : 529-547. doi: 10.3934/jimo.2015.11.529
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