%0 Journal Article
%A Azagra Rueda, Daniel
%A Ferrera Cuesta, Juan
%T Every closed convex set is the set of minimizers of some C1-smooth convex function
%D 2002
%@ 1088-6826
%U https://hdl.handle.net/20.500.14352/57021
%X The authors show that for every closed convex set C in a separable Banach space there is a nonnegative C1 convex function f such that C = {x: f(x) = 0}. The key is to show this for a closed halfspace. This result has several attractive consequences. For example, it provides an easy proof that every closed convex set is the Hausdorff limit of infinitely smooth convex bodies (Cn := {x: f(x) _ 1/n}) and that every continuous convex function is the Mosco limit of C1 convex functions.
%~