Answers are grounded in this paper and cite their sources.
The recently introduced proximal average of two convex functions is a convex function with many useful properties. In this paper, we introduce and systematically study the proximal average for finitely many convex functions. The basic properties of the proximal average with respect to the standard convex-analytical notions (domain, Fenchel conjugate, subdifferential, proximal mapping, epi-continuity, and others) are provided and illustrated by several examples.
No takes yet. Share an insight, caveat, or question.
Bauschke et al. (2008) studied this question.
Synapse has enriched 10 related papers. Consider them for comparative context: