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Added rho terms

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Andreas Tsouchlos 2023-04-18 20:59:56 +02:00
parent 6193b165ea
commit 0acc882dfe
1 changed files with 7 additions and 5 deletions
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latex/presentations/final/sections/lp_dec_using_admm.tex
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@ -706,9 +706,9 @@
\item Simplified rules% \item Simplified rules%
\footnote{$\left( \boldsymbol{z}_j \right)_i $ is a slight abuse of notation. \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 What is actually meant is the component of $\boldsymbol{z}_j$ that is associated
with the VN $i$, i.e., $\left( \boldsymbol{T}_j^\text{T} \boldsymbol{z}_j \right)_i$.\\ with the VN $i$, i.e., $\left( \boldsymbol{T}_j^\text{T}
The same is true for $\left( \boldsymbol{u}_j \right)_i$}% \boldsymbol{z}_j \right)_i$.\\
: The same is true for $\left( \boldsymbol{u}_j \right)_i$}:
\begin{alignat*}{3} \begin{alignat*}{3}
\tilde{c}_i &\leftarrow \frac{1}{\left| N_v\left( i \right) \right|} \left( \tilde{c}_i &\leftarrow \frac{1}{\left| N_v\left( i \right) \right|} \left(
@ -717,10 +717,12 @@
- \frac{\gamma_i}{\mu} \right) - \frac{\gamma_i}{\mu} \right)
\hspace{5mm} && \forall i\in\mathcal{I} \\ \hspace{5mm} && \forall i\in\mathcal{I} \\
\boldsymbol{z}_j &\leftarrow \Pi_{\mathcal{P}_{d_j}}\left( \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} \\ \hspace{5mm} && \forall j\in\mathcal{J} \\
\boldsymbol{u}_j &\leftarrow \boldsymbol{u}_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 - \boldsymbol{z}_j
\hspace{5mm} && \forall j\in\mathcal{J} \hspace{5mm} && \forall j\in\mathcal{J}
\end{alignat*} \end{alignat*}