2011 | OriginalPaper | Buchkapitel
Self-Dual Smooth Approximations of Convex Functions via the Proximal Average
verfasst von : Heinz H. Bauschke, Sarah M. Moffat, Xianfu Wang
Erschienen in: Fixed-Point Algorithms for Inverse Problems in Science and Engineering
Verlag: Springer New York
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The proximal average of two convex functions has proven to be a useful tool in convex analysis. In this note, we express the Goebel self-dual smoothing operator in terms of the proximal average, which allows us to give a different proof of self duality. We also provide a novel self-dual smoothing operator. Both operators are illustrated by smoothing the norm.