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

Lixin Shen, Guohui Song

We study the complete, possibly set-valued proximity operator of the nonconvex, scale-invariant ratio \(h(\vx)=\|\vx\|_{1}/\|\vx\|_{2}\). A polar decomposition of the nonzero branc…