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On Higher-Order Sensitivity Analysis in Nonsmooth Vector Optimization

Author

Listed:
  • H. T. H. Diem

    (College of Cantho)

  • P. Q. Khanh

    (International University of Hochiminh City)

  • L. T. Tung

    (Cantho University)

Abstract

We propose the notion of higher-order radial-contingent derivative of a set-valued map, develop some calculus rules and use them directly to obtain optimality conditions for several particular optimization problems. Then we employ this derivative together with contingent-type derivatives to analyze sensitivity for nonsmooth vector optimization. Properties of higher-order contingent-type derivatives of the perturbation and weak perturbation maps of a parameterized optimization problem are obtained.

Suggested Citation

  • H. T. H. Diem & P. Q. Khanh & L. T. Tung, 2014. "On Higher-Order Sensitivity Analysis in Nonsmooth Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 162(2), pages 463-488, August.
    • Handle: RePEc:spr:joptap:v:162:y:2014:i:2:d:10.1007_s10957-013-0424-3
    DOI: 10.1007/s10957-013-0424-3
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    References listed on IDEAS

    as
    1. P. Q. Khanh & N. D. Tuan, 2008. "Variational Sets of Multivalued Mappings and a Unified Study of Optimality Conditions," Journal of Optimization Theory and Applications, Springer, vol. 139(1), pages 47-65, October.
    2. N. L. H. Anh & P. Q. Khanh, 2013. "Variational Sets of Perturbation Maps and Applications to Sensitivity Analysis for Constrained Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 158(2), pages 363-384, August.
    3. T. D. Chuong & J. C. Yao, 2010. "Generalized Clarke Epiderivatives of Parametric Vector Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 146(1), pages 77-94, July.
    4. Nguyen Anh & Phan Khanh, 2013. "Higher-order optimality conditions in set-valued optimization using radial sets and radial derivatives," Journal of Global Optimization, Springer, vol. 56(2), pages 519-536, June.
    5. E. K. Makarov & N. N. Rachkovski, 1999. "Unified Representation of Proper Efficiency by Means of Dilating Cones," Journal of Optimization Theory and Applications, Springer, vol. 101(1), pages 141-165, April.
    6. A. B. Levy, 2001. "Lipschitzian Multifunctions and a Lipschitzian Inverse Mapping Theorem," Mathematics of Operations Research, INFORMS, vol. 26(1), pages 105-118, February.
    7. 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.
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    Cited by:

    1. Nguyen Xuan Duy Bao & Phan Quoc Khanh & Nguyen Minh Tung, 2022. "Quasi-contingent derivatives and studies of higher-orders in nonsmooth optimization," Journal of Global Optimization, Springer, vol. 84(1), pages 205-228, September.

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