A new method for strong-weak linear bilevel programming problem
Yue Zheng, Zhongping Wan, Shihui Jia, Guangmin Wang · Journal of Industrial and Management Optimization · 2014
We first propose an exact penalty method to solve strong-weak linearbilevel programming problem (for short, SWLBP) for every fixedcooperation degree from the follower. Then, we prove that the solution ofpenalized problem is also that of the original problem under someconditions. Furthermore, we give some properties of the optimalvalue function (as a function of the follower's cooperation degree)of SWLBP. Finally, we develop a method to acquire the criticalpoints of the optimal value function without enumerating all valuesof the cooperation degree from the follower, and thus this functionis also achieved. Numerical results show that the proposedmethods are feasible.