Table 1.

Pseudocode for solving PWLS_* using OS-SQS.

Precompute optimal curvatures

$c_i\left({\widehat{l}}_i\right)={\left[{\left[{\mathbf{W}}_{\ast }\right]}_i\right]}_{+}{\widehat{l}}_i\ge 0$

Precompute approximate dj term $d_j={\sum }_{i=1}^{N_y}{a}_{ij}{\gamma }_i{c}_i\left({\widehat{l}}_i\right)$

for each iteration n = 1, ..., niter

for each subset m = 1, ..., M

${\widehat{l}}_i={\sum }_{j=1}^{N_{\mu }}{a}_{ij}{\widehat{\mu }}_j{\stackrel{.}{h}}_i=w_i(l_i-{\widehat{l}}_i)\forall i\in S_m$

for j = 1, ..., Nμ

${\stackrel{.}{L}}_j=M{\sum }_{i\in S_m}{a}_{ij}{\stackrel{.}{h}}_i$

${\widehat{\mu }}_j={\left[{\widehat{\mu }}_j+\frac{{\stackrel{.}{L}}_j-{\beta }_R{\sum }_{k=1}^K{\left[{\Psi }_R\right]}_{kj}\stackrel{.}{H}\left({\left[{\Psi }_R\widehat{\mu }\right]}_k\right)}{d_j+2{\beta }_R{\sum }_{k=1}^K{\left[{\Psi }_R\right]}_{kj}^2{\omega }_H\left({\left[{\Psi }_R\widehat{\mu }\right]}_k\right)}\right]}_{+}$

end

end

end