Algorithm 1 ADMM [12]

$$\begin{array}{cc}\hfill & \mathbf{Require}:\ell (\cdot ;\mathit{y}),\rho (\cdot ),\beta ,\lambda ,{\mathit{v}}_0,{\mathit{u}}_0,\text{and}K\hfill \\ \hfill & 1:\mathbf{for}k=1,2,\dots ,K\mathbf{do}\hfill \\ \hfill & 2:{\mathit{x}}_k={\text{arg min}}_{\mathit{x}}\left\{\ell \right(\mathit{x};\mathit{y})+\frac{\beta }{2}\Vert \mathit{x}-{\mathit{v}}_{k-1}+{\mathit{u}}_{k-1}{\Vert }^2\}\hfill \\ \hfill & 3:{\mathit{v}}_k={\text{arg min}}_{\mathit{v}}\left\{\lambda \rho \right(\mathit{v})+\frac{\beta }{2}\Vert \mathit{v}-{\mathit{x}}_k-{\mathit{u}}_{k-1}{\Vert }^2\}\hfill \\ \hfill & 4:{\mathit{u}}_k={\mathit{u}}_{k-1}+{\mathit{x}}_k-{\mathit{v}}_k\hfill \\ \hfill & 5:\mathbf{end}\mathbf{for}\hfill \\ \hfill & 6:\text{Return}{x}_K\hfill \end{array}$$