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

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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.

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Yen, N.D. Stability of the Solution Set of Perturbed Nonsmooth Inequality Systems and Application. Journal of Optimization Theory and Applications 93, 199–225 (1997). https://doi.org/10.1023/A:1022662120550

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