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Sensitivity Analysis of a Stationary Point Set Map Under Total Perturbations. Part 2: Robinson Stability

Author

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  • Duong Thi Kim Huyen

    (Vietnam Academy of Science and Technology)

  • Jen-Chih Yao

    (China Medical University)

  • Nguyen Dong Yen

    (Vietnam Academy of Science and Technology)

Abstract

In Part 1 of this paper, we have estimated the Fréchet coderivative and the Mordukhovich coderivative of the stationary point set map of a smooth parametric optimization problem with one smooth functional constraint under total perturbations. From these estimates, necessary and sufficient conditions for the local Lipschitz-like property of the map have been obtained. In this part, we establish sufficient conditions for the Robinson stability of the stationary point set map. This allows us to revisit and extend several stability theorems in indefinite quadratic programming. A comparison of our results with the ones which can be obtained via another approach is also given.

Suggested Citation

  • Duong Thi Kim Huyen & Jen-Chih Yao & Nguyen Dong Yen, 2019. "Sensitivity Analysis of a Stationary Point Set Map Under Total Perturbations. Part 2: Robinson Stability," Journal of Optimization Theory and Applications, Springer, vol. 180(1), pages 117-139, January.
    • Handle: RePEc:spr:joptap:v:180:y:2019:i:1:d:10.1007_s10957-018-1295-4
    DOI: 10.1007/s10957-018-1295-4
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    References listed on IDEAS

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    1. Nguyen Thanh Qui, 2014. "Generalized Differentiation of a Class of Normal Cone Operators," Journal of Optimization Theory and Applications, Springer, vol. 161(2), pages 398-429, May.
    2. Nguyen Thanh Qui, 2016. "Coderivatives of implicit multifunctions and stability of variational systems," Journal of Global Optimization, Springer, vol. 65(3), pages 615-635, July.
    3. Stephen M. Robinson, 1980. "Strongly Regular Generalized Equations," Mathematics of Operations Research, INFORMS, vol. 5(1), pages 43-62, February.
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    Cited by:

    1. L. Q. Anh & T. Q. Duy & D. V. Hien, 2020. "Stability of efficient solutions to set optimization problems," Journal of Global Optimization, Springer, vol. 78(3), pages 563-580, November.

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