Abstract
For ill-posed bilevel programming problem, the optimistic solution is always the best decision for the upper level but it is not always the best choice for both levels if the authors consider the model’s satisfactory degree in application. To acquire a more satisfying solution than the optimistic one to realize the two levels’ most profits, this paper considers both levels’ satisfactory degree and constructs a minimization problem of the two objective functions by weighted summation. Then, using the duality gap of the lower level as the penalty function, the authors transfer these two levels problem to a single one and propose a corresponding algorithm. Finally, the authors give an example to show a more satisfying solution than the optimistic solution can be achieved by this algorithm.
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This research is supported by the National Science Foundation of China under Grant No. 71171150 and the National Natural Science Foundation of China, Tian Yuan Foundation under Grant No. 11226226.
This paper was recommended for publication by Editor DAI Yuhong.
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Jia, S., Wan, Z. A penalty function method for solving ill-posed bilevel programming problem via weighted summation. J Syst Sci Complex 26, 1019–1027 (2013). https://doi.org/10.1007/s11424-013-2248-5
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DOI: https://doi.org/10.1007/s11424-013-2248-5