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Optimality Conditions for Strictly Efficient Solutions in Set-valued Optimization

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Abstract

A new kind of tangent derivative, M-derivative, for set-valued function is introduced with help of a modified Dubovitskij-Miljutin cone. Several generalized pseudoconvex set-valued functions are introduced. When both the objective function and constraint function are M-derivative, under the assumption of near conesubconvexlikeness, by applying properties of the set of strictly efficient points and a separation theorem for convex sets, Fritz John and Kuhn-Tucker necessary optimality conditions are obtained for a point pair to be a strictly efficient element of set-valued optimization problem. Under the assumption of generalized pseudoconvexity, a Kuhn-Tucker sufficient optimality condition is obtained for a point pair to be a strictly efficient element of set-valued optimization problem.

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Authors and Affiliations

  1. Department of Mathematics, School of Sciences, Nanchang University, Nanchang, 330031, China

    Yi-hong Xu

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  1. Yi-hong Xu
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Correspondence to Yi-hong Xu.

Additional information

This research was supported by the National Natural Science Foundation of China Grant (11961047) and the Natural Science Foundation of Jiangxi Province (20192BAB201010).

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Xu, Yh. Optimality Conditions for Strictly Efficient Solutions in Set-valued Optimization. Acta Math. Appl. Sin. Engl. Ser. 36, 891–901 (2020). https://doi.org/10.1007/s10255-020-0971-y

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  • DOI: https://doi.org/10.1007/s10255-020-0971-y

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