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On Higher-Order Mixed Duality in Set-Valued Optimization

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Abstract

In the paper, we first develop sum and chain rules of higher-order radial derivatives. By virtue of these derivatives, we establish duality theorems for a primal-dual pair in set-valued optimization. Then, their applications to optimality conditions for weakly efficient solutions are implied. Our results are more advantageous than several existing ones in the literature, especially in case of the ordering cone in the constraint space having possibly empty interior.

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Acknowledgments

This study was supported by the project of the Moravian-Silesian Region, Czech Republic reg. no. 02692/2014/RRC. The author is grateful to two referees for their valuable remarks to improve the paper.

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Authors and Affiliations

  1. Department of Mathematics, University of Ostrava, 30. Dubna 22, 70103, Ostrava, Czech Republic

    Nguyen Le Hoang Anh

  2. Department of Optimization and System Theory, University of Science, Vietnam National University Hochiminh 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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Communicated by Anton Abdulbasah Kamil.

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Anh, N.L.H. On Higher-Order Mixed Duality in Set-Valued Optimization. Bull. Malays. Math. Sci. Soc. 41, 723–739 (2018). https://doi.org/10.1007/s40840-016-0362-y

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  • DOI: https://doi.org/10.1007/s40840-016-0362-y

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