Proximity Operator of the ${\ell }_1$ over ${\ell }_2$ Function

Lixin Shen, Guohui Song

We study the proximity operator of the nonconvex, scale-invariant ratio $h(\vx)=\|\vx\|_{1}/\|\vx\|_{2}$ and show it can be computed exactly in any dimension. By expressing $\vx=r\…