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@ -770,7 +770,7 @@ The steps to solve the dual problem then become:
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Luckily, the additional constaints only affect the $\boldsymbol{z}_j$-update steps.
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Furthermore, the $\boldsymbol{z}_j$-update steps can be shown to be equivalent to projections
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onto the check polytopes $\mathcal{P}_{d_j}$ \cite[Sec. III. B.]{original_admm}
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onto the check polytopes $\mathcal{P}_{d_j}$
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and the $\tilde{\boldsymbol{c}}$-update can be computed analytically%
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\footnote{In the $\tilde{c}_i$-update rule, the term
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@ -780,7 +780,7 @@ What is actually meant is the component of $\boldsymbol{z}_j$ that is associated
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with the variable node $i$, i.e., $\left( \boldsymbol{T}_j^\text{T}\boldsymbol{z}_j\right)_i$.
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The same is true for $\left( \boldsymbol{\lambda}_j \right)_i$.}
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\cite[Sec. III.]{lautern}:%
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\cite[Sec. III. B.]{original_admm}:%
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\begin{alignat*}{3}
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\tilde{c}_i &\leftarrow \frac{1}{\left| N_v\left( i \right) \right|} \left(
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