Radial soft thresholding
= Radial soft thresholding
{title2=$x\mapsto(1-\tau/\|x\|_2)_+x$}
The <proximal map> of $\tau\|\cdot\|_2$ sends $x$ to $(1-\tau/\|x\|_2)_+x$, with zero assigned at $x=0$. This removes vectors inside the radius-$\tau$ ball and shortens all larger vectors by a fixed radial distance. It is useful for groupwise sparsity.