Table 1.

Computational procedures of the Inexact augmented Lagrange multipliers (IALM) algorithm.

Algorithm: IALM
Input: Given a adjacency matrix A and parameter α = 0.1
Output:X*andE*
Initialize:$\text{X}=\mathrm{\text{0}},\text{E}=\mathrm{\text{0}},{\text{Y}}_1=\mathrm{\text{0}},{\text{Y}}_2=\mathrm{\text{0,}}\mu =\mathrm{\text{1}}{\mathrm{\text{0}}}^{-\mathrm{\text{4}}},{max}_{\mu }=\mathrm{\text{1}}{\mathrm{\text{0}}}^{\mathrm{\text{10}}},\rho =\mathrm{\text{1}}\mathrm{\text{.1}},\epsilon =\mathrm{\text{1}}{\mathrm{\text{0}}}^{-6}$
while ||A − AX − E||∞ ≥ ε and ||X − J||∞ ≥ ε do
a.$J=\arg \min \frac{1}{\mu }\Vert J{\Vert }_{*}+\frac{1}{2}{\Vert J-(X+Y_2/\mu )\Vert }_{\text{F}}^2$
b.$\text{X}=(\text{I}+{\text{A}}^T\text{A})({\text{A}}^T\text{A}-{\text{A}}^T\text{E}+\text{J}+({\text{A}}^T{Y}_1-{\text{Y}}_2)/\mu )$
c. $E=\arg \min \frac{\alpha }{\mu }\Vert E{\Vert }_{2,1}+\frac{1}{2}{\Vert E-(A-AX+Y_1/\mu )\Vert }_{\text{F}}^2$
d.Y1 = Y1 + μ(A − AX − E); Y2 = Y2 + μ(X − J)
e. μ = min(ρμ, maxμ)
end while