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Second-Order M-Composed Tangent Derivative and Its Applications

Author

Listed:
  • Yi-Hong Xu

    (Department of Mathematics, Nanchang University, Nanchang 330031, P. R. China)

  • Zhen-Hua Peng

    (Department of Mathematics, Nanchang University, Nanchang 330031, P. R. China)

Abstract

A new kind of second-order tangent derivative, second-order M-composed tangent derivative, for a set-valued function is introduced with help of a modified Dubovitskij–Miljutin cone. By using the concept, several generalized convex set-valued functions are introduced. When both the objective function and constrained function are second-order M-composed derivable, under the assumption of nearly cone-subconvexlikeness, by applying a separation theorem for convex sets, Fritz John and Kuhn–Tucker second-order necessary optimality conditions are obtained for a point pair to be a weak minimizer of set-valued optimization problem. Under the assumption of generalized pseudoconvexity, a Kuhn–Tucker second-order sufficient optimality condition is obtained for a point pair to be a weak minimizer of set-valued optimization problem. A unified second-order necessary and sufficient optimality condition is derived in terms of second-order M-composed tangent derivatives.

Suggested Citation

  • Yi-Hong Xu & Zhen-Hua Peng, 2018. "Second-Order M-Composed Tangent Derivative and Its Applications," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 35(05), pages 1-20, October.
    • Handle: RePEc:wsi:apjorx:v:35:y:2018:i:05:n:s021759591850029x
    DOI: 10.1142/S021759591850029X
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    References listed on IDEAS

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