Abstract
In this paper, we study Henig weakly efficient solutions for set-valued optimization problems. The connectedness of the Henig weakly efficient solution set is proved under the condition that the objective function be a cone-arcwise connected set-valued mapping. As an application of the result, we establish the connectedness of the set of super efficient solutions.
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Communicated by Jafar Zafarani.
The authors express their sincere gratitude to Professor J. Zafarani and the referees for comments and valuable suggestions. Q.S. Qiu was supported by the National Natural Science Foundation of China (Grant 11061023, 10831009), X.M. Yang was supported by the National Natural Science Foundation of China (Grant 10831009).
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Qiu, Q.S., Yang, X.M. Connectedness of Henig Weakly Efficient Solution Set for Set-Valued Optimization Problems. J Optim Theory Appl 152, 439–449 (2012). https://doi.org/10.1007/s10957-011-9906-3
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DOI: https://doi.org/10.1007/s10957-011-9906-3