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Higher-order optimality conditions in set-valued optimization using Studniarski derivatives and applications to duality

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Abstract

In this paper, we introduce upper and lower Studniarski derivatives of set-valued maps. By virtue of these derivatives, higher-order necessary and sufficient optimality conditions are obtained for several kinds of minimizers of a set-valued optimization problem. Then, applications to duality are given. Some remarks on several existent results and examples are provided to illustrate our results.

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Acknowledgments

We acknowledge Professor Szymon Dolecki’s very helpful discussions during our working. We are also grateful to an anonymous referee for his valuable remarks which helped to improve our previous manuscript.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, University of Science of Hochiminh City, 227 Nguyen Van Cu, District 5, Hochiminh City, Vietnam

    Nguyen Le Hoang Anh

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  1. Nguyen Le Hoang Anh
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Correspondence to Nguyen Le Hoang Anh.

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Anh, N.L.H. Higher-order optimality conditions in set-valued optimization using Studniarski derivatives and applications to duality. Positivity 18, 449–473 (2014). https://doi.org/10.1007/s11117-013-0254-4

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