Table III. Proposed OS-SQS methods with momentum in [17] (OS-mom1).

1: Initialize x(0) = z(0), t0 = 1 and compute D.

2: for n = 0, 1, …

3: for m = 0, 1, …, M − 1

4: k = nM + m

5: $t_{k+1}=\frac{1}{2}\left(1+\sqrt{1+4t_k^2}\right)$

6: ${\mathit{x}}^{(\frac{k+1}{M})}=\mathcal{P}\chi [{\mathit{z}}^{(\frac{k}{M})}-{\mathit{D}}^{-1}M\nabla {\mathrm{\Psi }}_m({\mathit{z}}^{(\frac{k}{M})})]$

7: ${\mathit{z}}^{(\frac{k+1}{M})}={\mathit{x}}^{(\frac{k+1}{M})}+\frac{t_{k-1}}{t_{k+1}}({\mathit{x}}^{(\frac{k+1}{M})}-{\mathit{x}}^{(\frac{k}{M})})$