Algorithm 1: Iterative algorithm for the prediction error optimization.

1 Initialization: Set ${\mathcal{L}}^{min}$ := +∞, $({\mathbf{x}}^{*},{\mathbf{t}}^{*},{\mathit{w}}^{*},{\mathit{u}}^{*})$ := $\mathbf{0}$

2 for each k $\in \mathcal{K}$ $\mathbf{do}$ {solving subproblem (19)}

3  Generating an initial points: Set k:= 0 and solve (20) to generate (${\mathbf{x}}^{\left(0\right)},{\mathit{\mu }}_m^{\left(0\right)},{\mathbf{w}}^{\left(0\right)},{\mathit{\mu }}_n^{\left(0\right)}$).

4  repeat

5   Solve (21) to obtain (${\mathbf{x}}^{*},{\mathit{\mu }}_m^{*},{\mathbf{w}}^{*},{\mathit{\mu }}_n^{*}$) and ${\mathcal{L}}^{(k+1)}$.

6   Update (${\mathbf{x}}^{(k+1)},{\mathit{\mu }}_m^{(k+1)},{\mathbf{w}}^{(k+1)},{\mathit{\mu }}_n^{(k+1)}$):=(${\mathbf{x}}^{*},{\mathit{\mu }}_m^{*},{\mathbf{w}}^{*},{\mathit{\mu }}_n^{*}$).

7   Set $k=k+1$.

8  until Convergence

9  if ${\mathcal{L}}^{\left(k\right)}<{\mathcal{L}}^{min}$ $\mathbf{then}$

10   Update ${\mathcal{L}}^{min}$ := ${\mathcal{L}}^{\left(k\right)}$ and (${\mathbf{x}}^{*},{\mathit{\mu }}_m^{*},{\mathbf{w}}^{*},{\mathit{\mu }}_n^{*}$):=(${\mathbf{x}}^{\left(k\right)},{\mathit{\mu }}_m^{\left(k\right)},{\mathbf{w}}^{\left(k\right)},{\mathit{\mu }}_n^{\left(k\right)}$).

11  end if

12 end for