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

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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.

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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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  1. Department of Optimization and System Theory, University of Science, Vietnam National University Ho Chi Minh City, 227 Nguyen Van Cu, District 5, Ho Chi Minh 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 for strict and weak efficient solutions in set-valued optimization. Positivity 20, 499–514 (2016). https://doi.org/10.1007/s11117-015-0369-x

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