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.
CITATION STYLE
Bauschke, H. H., Moffat, S. M., & Wang, X. (2011). Self-dual smooth approximations of convex functions via the proximal average. In Springer Optimization and Its Applications (Vol. 49, pp. 23–32). Springer International Publishing. https://doi.org/10.1007/978-1-4419-9569-8_2
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