2 citations · 3 across the 7 of their papers we have counts for
7 papers
Nearly convex sets: fine properties and domains or ranges of subdifferentials of convex functions
Sarah M. Moffat, Walaa M. Moursi, Xianfu Wang
Nearly convex sets play important roles in convex analysis, optimization and theory of monotone operators. We give a systematic study of nearly convex sets, and construct examples…
The resolvent average of monotone operators: dominant and recessive properties
Sedi Bartz, Heinz H. Bauschke, Sarah M. Moffat +1
Within convex analysis, a rich theory with various applications has been evolving since the proximal average of convex functions was first introduced over a decade ago. When one co…
Compositions and convex combinations of asymptotically regular firmly nonexpansive mappings are also asymptotically regular
Heinz H. Bauschke, Victoria Martin-Marquez, Sarah M. Moffat +1
Because of Minty's classical correspondence between firmly nonexpansive mappings and maximally monotone operators, the notion of a firmly nonexpansive mapping has proven to be of b…
Near equality, near convexity, sums of maximally monotone operators, and averages of firmly nonexpansive mappings
Heinz H. Bauschke, Sarah M. Moffat, Xianfu Wang
We study nearly equal and nearly convex sets, ranges of maximally monotone operators, and ranges and fixed points of convex combinations of firmly nonexpansive mappings. The main r…
Firmly nonexpansive mappings and maximally monotone operators: correspondence and duality
Heinz H. Bauschke, Sarah M. Moffat, Xianfu Wang
The notion of a firmly nonexpansive mapping is central in fixed point theory because of attractive convergence properties for iterates and the correspondence with maximal monotone…
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…