Subdifferential of the L1 norm
= Subdifferential of the L1 norm
{title2=$\partial\|\beta\|_1$}
The <subdifferential> of the <L1 norm> consists of vectors $z$ with $z_j=\operatorname{sgn}(\beta_j)$ when $\beta_j\ne0$ and $z_j\in[-1,1]$ when $\beta_j=0$. These coordinate conditions give the <Karush-Kuhn-Tucker conditions> for <Lasso> and <Square-root Lasso>.