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Coderivatives of implicit multifunctions and stability of variational systems

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  • Nguyen Thanh Qui

    (Can Tho University)

Abstract

We establish formulas for computing/estimating the regular and Mordukhovich coderivatives of implicit multifunctions defined by generalized equations in Asplund spaces. These formulas are applied to obtain conditions for solution stability of parametric variational systems over perturbed smooth-boundary constraint sets.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jglopt:v:65:y:2016:i:3:d:10.1007_s10898-015-0387-z
    DOI: 10.1007/s10898-015-0387-z
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    References listed on IDEAS

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    1. Hoai Le Thi & Tao Pham Dinh & Nguyen Yen, 2012. "Behavior of DCA sequences for solving the trust-region subproblem," Journal of Global Optimization, Springer, vol. 53(2), pages 317-329, June.
    2. 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.
    3. 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.
    4. Hoai Le Thi & Tao Pham Dinh & Nguyen Yen, 2011. "Properties of two DC algorithms in quadratic programming," Journal of Global Optimization, Springer, vol. 49(3), pages 481-495, March.
    5. 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.
    6. 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.
    7. Nguyen Qui, 2014. "Stability for trust-region methods via generalized differentiation," Journal of Global Optimization, Springer, vol. 59(1), pages 139-164, May.
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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.

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