Seonglae ChoA transformation function that smooths out discontinuous functions into their continuous counterparts.
Moreau envelope
The Moreau envelope (or the Moreau-Yosida regularization)
M
f
{\displaystyle M_{f}}
of a proper lower semi-continuous convex function
f
{\displaystyle f}
is a smoothed version of
f
{\displaystyle f}
. It was proposed by Jean-Jacques Moreau in 1965.
https://en.wikipedia.org/wiki/Moreau_envelope