What is the proximal operator of $ {\left\| x \right\|}_{2}^{3} $ where $ {\left\| x \right\|}_{2} $ is the $ {L}_{2} $ norm?
Using Moreau Decomposition (Someone needs to create a Wikipedia page for it) one could solve it as following:
$$ \operatorname{Prox}_{\lambda f \left( \cdot \right)} (v) = v - \Pi_B \left( v \right) $$
Where $ \Pi_B \left( \cdot \right) $ is the projection of onto the unit ball of the dual norm.
Yet I'm not sure how to derive for the case mentioned above.