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arXiv · 1003.5866

Self-dual Smooth Approximations of Convex Functions via the Proximal Average

Heinz H. Bauschke·Sarah M. Moffat·Xianfu Wang
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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.

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Heinz H. Bauschke, Sarah M. Moffat, Xianfu Wang. 2010-03-30. Self-dual Smooth Approximations of Convex Functions via the Proximal Average. https://arxiv.org/abs/1003.5866

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