Approximation of Functions and Sets
Jean‐Paul Penot, Constantin Zălinescu · 2001
In the present paper we tackle the problem of regularizing a quasiconvex function. We review some classical regularization processes, with this objective in view. One of them, the sublevel regularization seems to be adapted to quasiconvex functions in the sense that it preserves quasiconvexity. It is akin to the regularization of sets obtained by adding a small ball. We relate its regularizing effects to generalized differentiability properties of distance functions. We also review various processes for regularizing convex and generalized convex functions.