Input: $A\mathrm{,}b\mathrm{,}{x}_0$ parameter $\eta \in \left(\mathrm{0,1}\right]$ and $\lambda \in \left(\mathrm{0,2}\right)$ .

Output: the approximation solution $x_k$ of (1)

for $k=0,1,\cdots$ do until termination criterion is satisfied; do

Compute ${\epsilon }_k$ by (4);

Determine the control index set ${\mathcal{J}}_k$ by (3);

Update $x_{k+1}$ by (6).

end for