TY - JOUR AU - Azagra Rueda, Daniel AU - Ferrera Cuesta, Juan PY - 2002 DO - 10.1090/S0002-9939-02-06695-9 SN - 1088-6826 UR - https://hdl.handle.net/20.500.14352/57021 T2 - Proceedings of the American Mathematical Society 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.... LA - eng M2 - 3687 PB - America Mathematical Society TI - Every closed convex set is the set of minimizers of some C1-smooth convex function TY - journal article VL - 130 ER -