Implementation steps of GIREN algorithm
1)	Initialize coefficients β, and set the iteration index to 1. Define the convergence criteria variable crit, and set crit=0
2)	In the t -th iteration, fix all the βt and calculate the value of objective function F with (3).
3)	For j=1,⋯,m $$\begin{array}{c}f=2{\displaystyle \sum _{i=1}^n{x}_{ij}\left(y_i-{\beta }_0^t\right)}\\ e=2{\displaystyle \sum _{i=1}^n\left(x_{ij}^2-\gamma a_{ij}\right)+\lambda \left(1-\alpha \right)}\\ {\beta }_j^{t+1}=\{\begin{array}{cc}0& \text{when}\lambda \alpha >\left|f\right|\\ \frac{f-\lambda \alpha }{e}& \text{when}\lambda \alpha <\left|f\right|\text{and}f>0\\ \frac{f+\lambda \alpha }{e}& \text{when}\lambda \alpha <\left|f\right|\text{and}f<0\end{array}\end{array}$$ (6)
4)	Fix the updated βt+1, and calculate the value of the objective function. That is, update the value of objective function Fnew with (3).
5)	Update crit by (7). $$\mathit{\text{crit}}=\frac{F-F_{\mathit{\text{new}}}}{F}$$ (7)
6)	Repeat step 2)–5) until the convergence criterion is satisfied. That is, when crit is smaller than a predefined threshold.