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Positivity

, Volume 20, Issue 2, pp 499–514 | Cite as

Higher-order optimality conditions for strict and weak efficient solutions in set-valued optimization

  • Nguyen Le Hoang AnhEmail author
Article

Abstract

In this paper, we introduce a notion of higher-order Studniarski epiderivative of a set-valued map and study its properties. Then, we discuss their applications to optimality conditions in set-valued optimization. Higher-order optimality conditions for strict and weak efficient solutions of a constrained set-valued optimization problem are established. Some remarks on the existing results in the literature are given from our results.

Keywords

Higher-order Studniarski epiderivative Set-valued optimization problem Optimality condition Strict efficient solution Weak efficient solution C-preinvexity  

Mathematics Subject Classification

32F17 46G05 54C60 90C46 

Notes

Acknowledgments

This research was supported by Vietnam National University Hochiminh City (VNU-HCM) under grant number B2015-28-03. The author thanks an anonymous referee for helpful remarks and suggestions.

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Copyright information

© Springer Basel 2015

Authors and Affiliations

  1. 1.Department of Optimization and System TheoryUniversity of Science, Vietnam National University Ho Chi Minh CityHo Chi Minh CityVietnam

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