Convergence of a Proximal Point Method in the Presence of Computational Errors in Hilbert Spaces
SIAM Journal on Optimization
Information, Divergence and Risk for Binary Experiments
The Journal of Machine Learning Research
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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.