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Abstract: The proximal average of two convex functions has proven to be a useful toolin convex analysis. In this note, we express Goebel-s self-dual smoothingoperator in terms of the proximal average, which allows us to give a simpleproof of self duality. We also provide a novel self-dual smoothing operator.Both operators are illustrated by smoothing the norm.



Author: Heinz H. Bauschke, Sarah M. Moffat, Xianfu Wang

Source: https://arxiv.org/







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