期刊
JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION
卷 11, 期 2, 页码 529-547出版社
AMER INST MATHEMATICAL SCIENCES
DOI: 10.3934/jimo.2015.11.529
关键词
Bilevel programming; optimistic formulation; pessimistic formulation; partial cooperation; penalty method; critical point
类别
资金
- National Science Foundation of China [71171150, 71201146, 11226226]
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.
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