Algorithm 1:

ADMM for solving the constrained lasso (1).

1 Initialize β(0) = z(0) = β0, u(0) = 0, τ > 0;

2 repeat

3      ${\mathit{\beta }}^{(t+1)}\leftarrow \arg \min \frac{1}{2}\Vert \mathit{y}-\mathit{X}\mathit{\beta }{\Vert }_2^2+\frac{\tau }{2}\Vert \mathit{\beta }+{\mathit{z}}^{(t)}+{\mathit{u}}^{(t)}{\Vert }_2^2+\rho \Vert \mathit{\beta }{\Vert }_1;$

4      ${\mathit{z}}^{(t+1)}\leftarrow {\text{proj}}_{\mathcal{C}}\left({\mathit{\beta }}^{(t+1)}+{\mathit{u}}^{(t)}\right);$

5      u(t+1) ← u(t) + β(t+1) + z(t+1);

6 until convergence criterion is met;