Abstract. 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.
By nature, the proximal mapping of the proximal average for convex functions is exactly the convex combination of proximal mappings of individual convex functions REF .
The Proximal Average: Basic Theory
SIAM Journal on Optimization
SIAM Journal on Optimization
Computer Science Mathematics