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Second-Order Composed Contingent Derivative of the Perturbation Map in Multiobjective Optimization

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  • Zhenhua Peng

    (Department of Mathematics, School of Sciences, Nanchang University, Nanchang 330031, P. R. China2School of Mathematics and Statistics, Wuhan University, Wuhan 430072, P. R. China)

  • Zhongping Wan

    (School of Mathematics and Statistics, Wuhan University, Wuhan 430072, P. R. China)

Abstract

In view of the structural advantage of second-order composed derivatives, the purpose of this paper is to analyze quantitatively the behavior of perturbation maps for the first time by using this concept. First, new concepts of the second-order composed adjacent derivative and the second-order composed lower Dini derivative are introduced. Some relationships among the second-order composed contingent derivative, the second-order composed adjacent derivative and the second-order composed lower Dini derivative are discussed. Second, the relationships between second-order composed lower Dini derivable and Aubin property are provided. Third, by virtue of second-order composed contingent derivatives and the above relationships, some results concerning second-order sensitivity analysis are established without the assumption of the locally Lipschitz property or the locally Hölder continuity. Finally, we give some complete characterizations of second-order composed contingent derivatives of the perturbation maps.

Suggested Citation

  • Zhenhua Peng & Zhongping Wan, 2020. "Second-Order Composed Contingent Derivative of the Perturbation Map in Multiobjective Optimization," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 37(02), pages 1-23, March.
    • Handle: RePEc:wsi:apjorx:v:37:y:2020:i:02:n:s0217595920500025
    DOI: 10.1142/S0217595920500025
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    References listed on IDEAS

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    1. 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.
    2. S. Zhu & S. Li & K. Teo, 2014. "Second-order Karush–Kuhn–Tucker optimality conditions for set-valued optimization," Journal of Global Optimization, Springer, vol. 58(4), pages 673-692, April.
    3. Giancarlo Bigi & Marco Castellani, 2002. "K-epiderivatives for set-valued functions and optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 55(3), pages 401-412, June.
    4. Giancarlo Bigi & Marco Castellani, 2002. "K-epiderivatives for set-valued functions and optimization," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 55(3), pages 401-412, June.
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