\begin{algorithm}
\DontPrintSemicolon
\SetKwData{Left}{left}\SetKwData{This}{this}\SetKwData{Up}{up}
\SetKwFunction{Union}{Union}\SetKwFunction{FindCompress}{FindCompress}
\SetKwInOut{Input}{input}\SetKwInOut{Output}{output}
\Input{$w_0 \in \dom P_{\lambda} , \alpha_0 \in \dom D_{\lambda} $}
% \Output{$x$}
\BlankLine
\For{$t = 1,2,\ldots$ \KwTo converged}{
\If{Broadly working set algortm}{
$(w^{(t-1)}, \alpha^{(t-1)} ) \lA U^{(1)}(w^{(t-1)}, \alpha^{(t-1)}) $ \;
}
$(\cF^{(t)}, \cS^{(t)}) \lA (\cW_{\cF} (w^{(t-1)} ), \cW_{\cS} (\alpha^{(t-1)} ))$ \;
$(\hat{w}^{(0)}, \hat{\alpha}^{(0)} ) \leftarrow ({w}^{(t-1)} , {\alpha}^{(t-1)} )$\;
\For{$ u = 1,2, \ldots$ \KwTo until satisfy $C(\hat{w}^{(u)}, \hat{\alpha}^{(u)} ) $}{
$(\hat{w}^{(u)}, \hat{\alpha}^{(u)} ) \lA U^{(2)}(\hat{w}^{(u-1)}, \hat{\alpha}^{(u-1)}) $ \;
}
\uIf{Broadly working set algortm and $G_\lambda (\hat{w}^{(u)}, \hat{\alpha}^{(u)} ) > G_\lambda ({w}^{(t-1)}, {\alpha}^{(t-1)} )$}{
$({w}^{(t)}, {\alpha}^{(t)} ) \lA ({w}^{(t-1)}, {\alpha}^{(t-1)} )$\;
}
\uElse{
$({w}^{(t)}, {\alpha}^{(t)} ) \lA (\hat{w}^{(u)}, \hat{\alpha}^{(u)} )$\;
}
}
\caption{Strictly and Broadly Working Set Algorithm (Primal-Dual)}\label{alg:ws}
\end{algorithm}
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