The Proximal Average: Basic Theory
Heinz H. Bauschke, Rafal K. Goebel, Yves Lucet, Xianfu Wang · SIAM Journal on Optimization · 2008
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.