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Self-dual Smooth Approximations of Convex Functions via the Proximal Average
Heinz H. Bauschke, Sarah M. Moffat, Xianfu Wang
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 proxi…
Compositions and Averages of Two Resolvents: Relative Geometry of Fixed Points Sets and a Partial Answer to a Question by C. Byrne
Xianfu Wang, Heinz H. Bauschke
We show that the set of fixed points of the average of two resolvents can be found from the set of fixed points for compositions of two resolvents associated with scaled monotone o…
On the maximal monotonicity of the sum of a maximal monotone linear relation and the subdifferential operator of a sublinear function
Heinz H. Bauschke, Xianfu Wang, Liangjin Yao
The most important open problem in Monotone Operator Theory concerns the maximal monotonicity of the sum of two maximal monotone operators provided that Rockafellar's constraint qu…