I am working through some infimal convolution examples and came across this one:
$$f = |x| + \frac{|x|^3}{3}$$ where the Moreau envelope $f_\mu$ has to be computed. When using a naive approach where i use the (sub)derivatives of
$$ |y| + \frac{|y|^3}{3} + \frac{1}{2\mu} ||x-y||^2 $$ I do not get far. Does someone have a better solution?
Thanks!