A NEW METHOD FOR STRONG-WEAK LINEAR BILEVEL PROGRAMMING PROBLEM

作者：Zheng Yue^*; Wan Zhongping; Jia Shihui; Wang Guangmin

来源：Journal of Industrial and Management Optimization, 2015, 11(2): 529-547.

DOI：10.3934/jimo.2015.11.529

• Bilevel programming
• optimistic formulation
• pessimistic formulation
• partial cooperation
• penalty method
• critical point

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 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.

• 出版日期2015-4
• 单位中国地质大学（北京）; 武汉大学; 武汉科技大学; 黄冈师范学院