On the interchange of subdifferentiation and epi-convergence (Q1910084)

As the title of the paper clearly claimes, conditions are investigated that guarantee the interchange of the subdifferentiation notion and the epi-convergence notion. In particular, the Fréchet subdifferentiation, the limiting subdifferential, and the Clarke subdifferential are considered. An interesting application is given to the second-order derivative, that is, when the tangent cone of the subdifferential of a function at some point is equal to or included in the subdifferential of the second (lower) epi-derivative of the function.