Input: X, Y and tol. Choose ${\lambda }_1>0,\mu >0$ and $\rho >\rho \left(X^{\text{T}}X+{\lambda }_1^2{I}_p\right)$ , where $\rho (\cdot )$ denotes the spectral radius, select $\left(X^0,Y^0,{\lambda }^0\right)=\left(0,0,0\right)$ for $k=1,2,\cdots ,N$

‘do

Compute $X^{k+1}$ by (27).

Compute $Y^{k+1}$ by (28).

end

Update ${\lambda }^{k+1}={\lambda }^k-\mu \left(Y^{k+1}-D{X}^{k+1}\right)$ ;

end

Output: $\left(X^N,Y^N,{\lambda }^N\right)$ as an approximate solution of (11).