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Azagra Rueda, Daniel and Ferrera Cuesta, Juan
(2002)
*Every closed convex set is the set of minimizers of some C1-smooth convex function.*
Proceedings of the American Mathematical Society, 130
(12).
pp. 3687-3692.
ISSN 1088-6826

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Official URL: http://www.ams.org/proc/

## 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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