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Second-Order Differential and Sensitivity Properties of Weak Vector Variational Inequalities

Author

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  • M. H. Li

    (Chongqing University)

  • S. J. Li

    (Chongqing University)

Abstract

In this paper, by using the second-order contingent derivative, second-order differential properties of a class of set-valued maps are investigated and an explicit expression of the second-order contingent derivatives is obtained. Then, by means of a gap function, second-order sensitivity properties are discussed for a weak vector variational inequality.

Suggested Citation

  • M. H. Li & S. J. Li, 2010. "Second-Order Differential and Sensitivity Properties of Weak Vector Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 144(1), pages 76-87, January.
    • Handle: RePEc:spr:joptap:v:144:y:2010:i:1:d:10.1007_s10957-009-9592-6
    DOI: 10.1007/s10957-009-9592-6
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    References listed on IDEAS

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    1. S. J. Li & K. L. Teo & X. Q. Yang, 2008. "Higher-Order Optimality Conditions for Set-Valued Optimization," Journal of Optimization Theory and Applications, Springer, vol. 137(3), pages 533-553, June.
    2. P. Q. Khanh & N. D. Tuan, 2008. "Higher-Order Variational Sets and Higher-Order Optimality Conditions for Proper Efficiency in Set-Valued Nonsmooth Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 139(2), pages 243-261, November.
    3. V. Kalashnikov & B. Jadamba & A. A. Khan, 2006. "First and second order optimality conditions in set optimization," Springer Optimization and Its Applications, in: Stephan Dempe & Vyacheslav Kalashnikov (ed.), Optimization with Multivalued Mappings, pages 265-276, Springer.
    4. J. Jahn & A. A. Khan & P. Zeilinger, 2005. "Second-Order Optimality Conditions in Set Optimization," Journal of Optimization Theory and Applications, Springer, vol. 125(2), pages 331-347, May.
    5. K. L. Lin & D. P. Yang & J. C. Yao, 1997. "Generalized Vector Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 92(1), pages 117-125, January.
    6. S. J. Li & Hong Yan & G. Y. Chen, 2003. "Differential and sensitivity properties of gap functions for vector variational inequalities," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 57(3), pages 377-391, August.
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    Cited by:

    1. Xiang-Kai Sun & Sheng-Jie Li, 2014. "Generalized second-order contingent epiderivatives in parametric vector optimization problems," Journal of Global Optimization, Springer, vol. 58(2), pages 351-363, February.

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