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New Second-Order Tangent Epiderivatives and Applications to Set-Valued Optimization

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  • Zhenhua Peng

    (Nanchang University)

  • Yihong Xu

    (Nanchang University)

Abstract

A new second-order tangent set is introduced, with which a new second-order tangent epiderivative is also introduced for a set-valued map. Applying a separation theorem for convex sets, second-order Fritz John and Kuhn–Tucker necessary optimality conditions are obtained for a point pair to be a weak minimizer of set-valued optimization problem. Under the assumption of lower semicontinuous, a second-order Kuhn–Tucker sufficient optimality condition is obtained for a point pair to be a weak minimizer of set-valued optimization problem.

Suggested Citation

  • Zhenhua Peng & Yihong Xu, 2017. "New Second-Order Tangent Epiderivatives and Applications to Set-Valued Optimization," Journal of Optimization Theory and Applications, Springer, vol. 172(1), pages 128-140, January.
    • Handle: RePEc:spr:joptap:v:172:y:2017:i:1:d:10.1007_s10957-016-1011-1
    DOI: 10.1007/s10957-016-1011-1
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    References listed on IDEAS

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    Cited by:

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