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Optimality conditions in set optimization employing higher-order radial derivatives

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Abstract

There are two approaches of defining the solutions of a set-valued optimization problem: vector criterion and set criterion. This note is devoted to higher-order optimality conditions using both criteria of solutions for a constrained set-valued optimization problem in terms of higher-order radial derivatives. In the case of vector criterion, some optimality conditions are derived for isolated (weak) minimizers. With set criterion, necessary and sufficient optimality conditions are established for minimal solutions relative to lower set-order relation.

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Acknowledgements

The author would like to extend sincere gratitude to Prof. Qinghong Zhang and Dr. Truong Q. Bao (Department of Mathematics & Computer Science, Northern Michigan University, USA) for their assistance. The author is grateful to the anonymous referees for their helpful comments and suggestions.

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Authors and Affiliations

  1. Department of Mathematics, Beifang University of Nationalities, Yinchuan, 750021, China

    Guo-lin Yu

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  1. Guo-lin Yu
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Correspondence to Guo-lin Yu.

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Supported by the National Natural Science Foundation of China (11361001), Natural Science Foundation of Ningxia (NZ14101).

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Yu, Gl. Optimality conditions in set optimization employing higher-order radial derivatives. Appl. Math. J. Chin. Univ. 32, 225–236 (2017). https://doi.org/10.1007/s11766-017-3414-7

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  • DOI: https://doi.org/10.1007/s11766-017-3414-7

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