Set-Valued Analysis

, Volume 2, Issue 1, pp 381–393

Convergence of generalized gradients

  • Tullio Zolezzi

DOI: 10.1007/BF01027113

Cite this article as:
Zolezzi, T. Set-Valued Anal (1994) 2: 381. doi:10.1007/BF01027113


For the graphs of Clarke's generalized gradients we prove that
$$lim sup_{n \to + \infty } gph \partial f_n \subset gph \partial f in (E, strong) \times (E^* , weak).$$
provided that the sequencefn 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.

Mathematics Subject Classification (1991)


Key words

Generalized gradientepi-convergencestability of multipliersintegral functionals

Copyright information

© Kluwer Academic Publishers 1994

Authors and Affiliations

  • Tullio Zolezzi
    • 1
  1. 1.Dipartimento di MatematicaGenovaItaly