Self-dual Smooth Approximations of Convex Functions via the Proximal Average
Functional Analysis
2010-03-31 v1 Optimization and Control
Abstract
The proximal average of two convex functions has proven to be a useful tool in convex analysis. In this note, we express Goebel's self-dual smoothing operator in terms of the proximal average, which allows us to give a simple proof of self duality. We also provide a novel self-dual smoothing operator. Both operators are illustrated by smoothing the norm.
Keywords
Cite
@article{arxiv.1003.5866,
title = {Self-dual Smooth Approximations of Convex Functions via the Proximal Average},
author = {Heinz H. Bauschke and Sarah M. Moffat and Xianfu Wang},
journal= {arXiv preprint arXiv:1003.5866},
year = {2010}
}