Lipschitz behaviour of the Legendre-Fenchel transform
An estimate of the modulus of continuity of the Legendre-Fenchel transform, acting on the set of extended real-valued convex functions, is given. The functions are defined on a normed vector space or on its dual space equipped with the Attouch-Wets topology. It is proved further that the Legendre-Fenchel transform has a locally Lipschitz behaviour when the set of closed proper convex functions is endowed with suitable families of semimetrics.
scientific article; zbMATH DE number 627462
scientific article