RT Journal Article
T1 Every closed convex set is the set of minimizers of some C1-smooth convex function
A1 Azagra Rueda, Daniel
A1 Ferrera Cuesta, Juan
AB 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.
PB America Mathematical Society
SN 1088-6826
YR 2002
FD 2002
LK https://hdl.handle.net/20.500.14352/57021
UL https://hdl.handle.net/20.500.14352/57021
LA eng
DS Docta Complutense
RD 7 abr 2025