Abstract
For the graphs of Clarke's generalized gradients we prove that
provided that the sequencef n of locally Lipschitz functions on a Banach spaceE with separable dual is strongly epi-convergent tof, equi-lower semidifferentiable and locally equibounded. This result extends [21] to the infinite-dimensional setting, and finds applications to the continuous behavior of the multiplier rule and of the generalized gradients of integral functionals under data perturbations.
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Zolezzi, T. Convergence of generalized gradients. Set-Valued Anal 2, 381–393 (1994). https://doi.org/10.1007/BF01027113
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DOI: https://doi.org/10.1007/BF01027113