, Volume 18, Issue 3, pp 449–473 | Cite as

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

  • Nguyen Le Hoang AnhEmail author


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.


Studniarski derivatives Optimality conditions Set-valued optimization problem Efficiency Generalized subconvexlike Duality 

Mathematics Subject Classification (2010)

32F17 46G05 90C29 90C46 



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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Copyright information

© Springer Basel 2013

Authors and Affiliations

  1. 1.Department of Mathematics and Computer ScienceUniversity of Science of Hochiminh CityHochiminh CityVietnam

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