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Higher-order optimality conditions for proper efficiency in nonsmooth vector optimization using radial sets and radial derivatives

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Abstract

We establish both necessary and sufficient optimality conditions of higher orders for various kinds of proper solutions to nonsmooth vector optimization in terms of higher-order radial sets and radial derivatives. These conditions are for global solutions and do not require continuity and convexity assumptions. Examples are provided to show advantages of the results over existing ones in a number of cases.

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Acknowledgments

This research was funded by Vietnam National University Hochiminh City (VNU-HCM) under grant number B2013-28-01. The authors would like to thank the Editor and Anonymous Referees for their valuable remarks and suggestions, which have helped them to improve the paper.

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Authors and Affiliations

  1. Department of Optimization and System Theory, University of Science of Hochiminh City, 227 Nguyen Van Cu, District 5, Hochiminh City, Vietnam

    Nguyen Le Hoang Anh

  2. Department of Mathematics, International University of Hochiminh City, Linh Trung, Thu Duc, Hochiminh City, Vietnam

    Phan Quoc Khanh

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  1. Nguyen Le Hoang Anh
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  2. Phan Quoc Khanh
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Correspondence to Nguyen Le Hoang Anh.

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Le Hoang Anh, N., Khanh, P.Q. Higher-order optimality conditions for proper efficiency in nonsmooth vector optimization using radial sets and radial derivatives. J Glob Optim 58, 693–709 (2014). https://doi.org/10.1007/s10898-013-0077-7

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  • DOI: https://doi.org/10.1007/s10898-013-0077-7

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