Algorithm 1: Block coordinate descent algorithm

1. Set initial value for ${}^0\in {\mathbb{R}}^{2p}\mathrm{and}{\rho }^0\in (0,1)$; 2. $\mathit{repeat}$ $\{\mathrm{For}k=0,1,2,\cdots \}$ 3.      Solve the subproblem about $\rho$ with initial point ${\rho }^k$: $${\rho }^{k+1}\leftarrow \underset{\rho \in [0,1]}{min}L\left({\tilde{\beta }}^k,\rho \right)$$ (8) 4.      Solve the subproblem with initial value ${\tilde{\beta }}^k$, $${\beta }^{k+1}\leftarrow \underset{\tilde{\beta }\in R^{2p}}{min}L\left(\tilde{\beta },{\rho }^{k+1}\right)$$ (9)       to obtain a solution ${\tilde{\beta }}^{k+1}$, ensuring that $L\left({\tilde{\beta }}^k,{\rho }^{k+1}\right)-L\left({\tilde{\beta }}^{k+1},{\rho }^{k+1}\right)\le 0$, and ${\tilde{\beta }}^{k+1}$ is a stationary point of $L\left(\tilde{\beta },{\rho }^{k+1}\right)$. 5. $\mathit{until}$ convergence.