diff --git a/latex/presentations/final/sections/lp_dec_using_admm.tex b/latex/presentations/final/sections/lp_dec_using_admm.tex
index da54d54..ef8f230 100644
--- a/latex/presentations/final/sections/lp_dec_using_admm.tex
+++ b/latex/presentations/final/sections/lp_dec_using_admm.tex
@@ -706,9 +706,9 @@
         \item Simplified rules%
             \footnote{$\left( \boldsymbol{z}_j \right)_i $ is a slight abuse of notation.
             What is actually meant is the component of $\boldsymbol{z}_j$ that is associated
-            with the VN $i$, i.e., $\left( \boldsymbol{T}_j^\text{T} \boldsymbol{z}_j \right)_i$.\\
-            The same is true for $\left( \boldsymbol{u}_j \right)_i$}%
-            :
+            with the VN $i$, i.e., $\left( \boldsymbol{T}_j^\text{T}
+                \boldsymbol{z}_j \right)_i$.\\
+            The same is true for $\left( \boldsymbol{u}_j \right)_i$}:
 
             \begin{alignat*}{3}
                 \tilde{c}_i &\leftarrow \frac{1}{\left| N_v\left( i \right) \right|} \left( 
@@ -717,10 +717,12 @@
                     - \frac{\gamma_i}{\mu} \right)
                 \hspace{5mm} && \forall i\in\mathcal{I} \\
                 \boldsymbol{z}_j &\leftarrow \Pi_{\mathcal{P}_{d_j}}\left(
-                    \boldsymbol{T}_j\tilde{\boldsymbol{c}} + \boldsymbol{u}_j \right)
+                    \rho \boldsymbol{T}_j\tilde{\boldsymbol{c}} - \boldsymbol{z}_j
+                    \left( 1-\rho \right) + \boldsymbol{u}_j \right)
                 \hspace{5mm} && \forall j\in\mathcal{J} \\
                 \boldsymbol{u}_j &\leftarrow \boldsymbol{u}_j
-                    + \boldsymbol{T}_j\tilde{\boldsymbol{c}}
+                    + \rho \boldsymbol{T}_j\tilde{\boldsymbol{c}}
+                    - \left( 1-\rho \right) \boldsymbol{z}_j
                     - \boldsymbol{z}_j
                 \hspace{5mm} && \forall j\in\mathcal{J}
             \end{alignat*}