Abstract
In this paper, we propose several second-order derivatives for set-valued maps and discuss their properties. By using these derivatives, we obtain second-order necessary optimality conditions for strict efficiency of a set-valued optimization problem with inclusion constraints in real normed spaces. We also establish second-order sufficient optimality conditions for strict efficiency of the set-valued optimization problem in finite-dimensional normed spaces. As applications, we investigate second-order sufficient and necessary optimality conditions for a strict local efficient solution of order two of a nonsmooth vector optimization problem with an abstract set and a functional constraint.
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Acknowledgements
This research was supported by the National Natural Science Foundation of China (Grants 10871216 and 11171362) and the Fundamental Research Funds for the Central Universities (Grant: CDJXS11100017). The authors thank the two anonymous reviewers for their valuable comments and suggestions, which helped to improve the paper.
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Communicated by Johannes Jahn.
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Li, S.J., Zhu, S.K. & Li, X.B. Second-Order Optimality Conditions for Strict Efficiency of Constrained Set-Valued Optimization. J Optim Theory Appl 155, 534–557 (2012). https://doi.org/10.1007/s10957-012-0076-8
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DOI: https://doi.org/10.1007/s10957-012-0076-8