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Generalized Differentiation of a Class of Normal Cone Operators

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  • Nguyen Thanh Qui

    (Can Tho University)

Abstract

This paper investigates generalized differentiation of normal cone operators to parametric smooth-boundary sets in Asplund spaces. We obtain formulas for computing the Fréchet and Mordukhovich coderivatives of such normal cone operators. We also give several examples to illustrate how the formulas can be used in practical calculations and applications.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:161:y:2014:i:2:d:10.1007_s10957-013-0427-0
    DOI: 10.1007/s10957-013-0427-0
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    References listed on IDEAS

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    1. Nguyen Qui, 2013. "Variational inequalities over Euclidean balls," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 78(2), pages 243-258, October.
    2. J.-C. Yao & N. D. Yen, 2010. "Parametric Variational System with a Smooth-Boundary Constraint Set," Springer Optimization and Its Applications, in: Regina S. Burachik & Jen-Chih Yao (ed.), Variational Analysis and Generalized Differentiation in Optimization and Control, pages 205-221, Springer.
    3. Nguyen Thanh Qui, 2012. "Nonlinear Perturbations of Polyhedral Normal Cone Mappings and Affine Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 153(1), pages 98-122, April.
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    Cited by:

    1. Duong Thi Kim Huyen & Jen-Chih Yao & Nguyen Dong Yen, 2019. "Sensitivity Analysis of a Stationary Point Set Map Under Total Perturbations. Part 1: Lipschitzian Stability," Journal of Optimization Theory and Applications, Springer, vol. 180(1), pages 91-116, January.
    2. 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.
    3. V. D. Thinh & T. D. Chuong & N. L. H. Anh, 2023. "Second order analysis for robust inclusion systems and applications," Journal of Global Optimization, Springer, vol. 85(1), pages 81-110, January.
    4. 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.

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    1. 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.
    2. Duong Thi Kim Huyen & Jen-Chih Yao & Nguyen Dong Yen, 2019. "Sensitivity Analysis of a Stationary Point Set Map Under Total Perturbations. Part 1: Lipschitzian Stability," Journal of Optimization Theory and Applications, Springer, vol. 180(1), pages 91-116, January.
    3. Nguyen Qui, 2013. "Variational inequalities over Euclidean balls," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 78(2), pages 243-258, October.
    4. Nguyen Dong Yen & Xiaoqi Yang, 2018. "Affine Variational Inequalities on Normed Spaces," Journal of Optimization Theory and Applications, Springer, vol. 178(1), pages 36-55, July.

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