Azagra Rueda, Daniel and Ferrera Cuesta, Juan (2002) Every closed convex set is the set of minimizers of some C1smooth convex function. Proceedings of the American Mathematical Society, 130 (12). pp. 36873692. ISSN 10886826

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Abstract
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.
Item Type:  Article 

Subjects:  Sciences > Mathematics > Functional analysis and Operator theory 
ID Code:  12354 
Deposited On:  07 Mar 2011 12:04 
Last Modified:  06 Feb 2014 09:23 
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