未命名

$${\mathbf{x}}_{i\ast }^{\left(k+1\right)}:=\text{arg}\underset{{\mathbf{x}}_{i\ast }\in {\mathbf{X}}_{i\ast }}{\min }\left(f_i\left({\mathbf{x}}_{i\ast }\right)+\frac{\rho }{2}\Vert {\mathbf{R}}_i{\mathbf{x}}_{i\ast }-{\mathbf{r}}_i+{\mathbf{\alpha }}_i^{\left(k\right)}{\Vert }_2^2+\frac{\rho }{2}\Vert {\mathbf{x}}_{i\ast }-{\mathbf{z}}_{i\ast }^{\left(k\right)}+{\mathbf{\lambda }}_{i\ast }^{\left(k\right)}{\Vert }_2^2\right),\forall i$$

${\mathbf{z}}_{\ast j}^{(k+1)}:=\text{arg}{\min }_{{\mathbf{z}}_{\ast j}}\left(g_j({\mathbf{z}}_{\ast j})+\frac{\rho }{2}\Vert {\mathbf{D}}_j{\mathbf{z}}_{\ast j}-{\mathbf{d}}_j+{\mathbf{\beta }}_j^{(k)}{\Vert }_2^2+\frac{\rho }{2}\Vert {\mathbf{z}}_{\ast j}-{\mathbf{x}}_{\ast j}^{(k+1)}-{\mathbf{\lambda }}_{\ast j}^{(k)}{\Vert }_2^2\right),\forall j$