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Stability of the Solution Set of Perturbed Nonsmooth Inequality Systems and Application

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  • N. D. Yen

    (National Center for Natural Science and Technology)

Abstract

Stability properties of the solution set of generalized inequality systems with locally Lipschitz functions are obtained under a regularity condition on the generalized Jacobian and the Clarke tangent cone. From these results, we derive sufficient conditions for the optimal value function in a nonsmooth optimization problem to be continuous or locally Lipschitz at a given parameter.

Suggested Citation

  • N. D. Yen, 1997. "Stability of the Solution Set of Perturbed Nonsmooth Inequality Systems and Application," Journal of Optimization Theory and Applications, Springer, vol. 93(1), pages 199-225, April.
    • Handle: RePEc:spr:joptap:v:93:y:1997:i:1:d:10.1023_a:1022662120550
    DOI: 10.1023/A:1022662120550
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    References listed on IDEAS

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    1. Jean-Pierre Aubin, 1984. "Lipschitz Behavior of Solutions to Convex Minimization Problems," Mathematics of Operations Research, INFORMS, vol. 9(1), pages 87-111, February.
    2. A. Jourani & L. Thibault, 1993. "Approximations and Metric Regularity in Mathematical Programming in Banach Space," Mathematics of Operations Research, INFORMS, vol. 18(2), pages 390-401, May.
    3. Asen L. Dontchev & William W. Hager, 1994. "Implicit Functions, Lipschitz Maps, and Stability in Optimization," Mathematics of Operations Research, INFORMS, vol. 19(3), pages 753-768, August.
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    Cited by:

    1. N. Huy & D. Kim, 2013. "Lipschitz behavior of solutions to nonconvex semi-infinite vector optimization problems," Journal of Global Optimization, Springer, vol. 56(2), pages 431-448, June.
    2. Gui-Hua Lin & Mei-Ju Luo & Jin Zhang, 2016. "Smoothing and SAA method for stochastic programming problems with non-smooth objective and constraints," Journal of Global Optimization, Springer, vol. 66(3), pages 487-510, November.
    3. A. Uderzo, 2014. "On Lipschitz Semicontinuity Properties of Variational Systems with Application to Parametric Optimization," Journal of Optimization Theory and Applications, Springer, vol. 162(1), pages 47-78, July.
    4. Vu Thi Huong & Jen-Chih Yao & Nguyen Dong Yen, 2017. "On the Stability and Solution Sensitivity of a Consumer Problem," Journal of Optimization Theory and Applications, Springer, vol. 175(2), pages 567-589, November.
    5. Nguyen Ngoc Luan & Do Sang Kim & Nguyen Dong Yen, 2022. "Two Optimal Value Functions in Parametric Conic Linear Programming," Journal of Optimization Theory and Applications, Springer, vol. 193(1), pages 574-597, June.

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