Added frame comparing the decoding algorithms in their proximal form

latex/presentations/final/sections/decoding_algorithms.tex

@@ -840,7 +840,82 @@ return $\boldsymbol{\hat{c}}$
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \begin{frame}[t, fragile]
-    \frametitle{Comparison of Proximal Decoding and \\LP Decoding using ADMM}
+    \frametitle{Comparison of Proximal Decoding and\\LP Decoding using ADMM}
+
+    \vspace*{-1cm}
+
+    \begin{figure}[h]
+    \centering
+   
+    \begin{subfigure}[b]{0.47\textwidth}
+        \centering
+   
+        \begin{align*}
+            \text{minimize}\hspace{2mm}   & \textcolor{KITblue}{\underbrace{L\left(
+                    \boldsymbol{y} \mid \tilde{\boldsymbol{x}} \right)}_{\text{Likelihood}}}
+                    + \textcolor{KITred}{\underbrace{\gamma h\left( \tilde{\boldsymbol{x}}
+                        \right)} _{\text{Constraints}}} \\
+            \text{subject to}\hspace{2mm} &\tilde{\boldsymbol{x}} \in \mathbb{R}^n
+        \end{align*}
+       
+        \vspace*{-5mm}
+
+        \begin{algorithm}[caption={}, label={},
+            basicstyle=\fontsize{10}{18}\selectfont
+            ]
+Initialize $\boldsymbol{r}, \boldsymbol{s}, \omega, \gamma$
+while stopping critierion unfulfilled do
+    $\textcolor{KITblue}{\boldsymbol{r} \leftarrow \boldsymbol{r}
+        + \omega \nabla L\left( \boldsymbol{y} \mid \boldsymbol{s} \right)} $
+    $\textcolor{KITred}{\boldsymbol{s} \leftarrow
+        \textbf{prox}_{\gamma h}\left( \boldsymbol{r} \right)} $|\Suppressnumber|
+|\Reactivatenumber|
+end while
+return $\boldsymbol{s}$
+        \end{algorithm}
+    \end{subfigure}\hfill%
+    \begin{subfigure}[b]{0.5\textwidth}
+        \centering
+        
+        \begin{align*}
+            \text{minimize}\hspace{5mm} &
+                \textcolor{KITblue}{\underbrace{\boldsymbol{\gamma}^\text{T}
+                    \tilde{\boldsymbol{c}}}_{\text{Likelihood}}}
+                + \textcolor{KITred}{\underbrace{\sum\nolimits_{j\in\mathcal{J}}
+                    g_j\left( \boldsymbol{T}_j\tilde{\boldsymbol{c}}
+                    \right)}_{\text{Constraints}}} \\
+            \text{subject to}\hspace{5mm} &
+                \tilde{\boldsymbol{c}} \in \mathbb{R}^n
+        \end{align*}
+        
+        \vspace*{-5mm}
+    
+        \begin{algorithm}[caption={}, label={},
+            basicstyle=\fontsize{10}{18}\selectfont
+            ]
+Initialize $\tilde{\boldsymbol{c}}, \boldsymbol{z}, \boldsymbol{u}, \boldsymbol{\gamma}, \rho$
+while stopping criterion unfulfilled do
+    $\textcolor{KITblue}{\tilde{\boldsymbol{c}} \leftarrow \argmin_{\tilde{\boldsymbol{c}}}
+        \left( \boldsymbol{\gamma}^\text{T}\tilde{\boldsymbol{c}}
+        + \frac{\rho}{2}\sum_{j\in\mathcal{J}} \left\Vert
+            \boldsymbol{T}_j\tilde{\boldsymbol{c}} - \boldsymbol{z}_j
+            + \boldsymbol{u}_j \right\Vert \right)}$
+    $\textcolor{KITred}{\boldsymbol{z}_j \leftarrow \textbf{prox}_{g_j}
+        \left( \boldsymbol{T}_j\tilde{\boldsymbol{c}}
+        + \boldsymbol{u}_j \right), \hspace{5mm}\forall j\in\mathcal{J}}$
+    $\boldsymbol{u}_j \leftarrow \boldsymbol{u}_j
+        + \tilde{\boldsymbol{c}} - \boldsymbol{z}_j, \hspace{14.5mm}\forall j\in\mathcal{J}$
+end while
+return $\tilde{\boldsymbol{c}}$
+        \end{algorithm}
+    \end{subfigure}%
+\end{figure}%
+
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[t, fragile]
+    \frametitle{Comparison of Proximal Decoding and\\LP Decoding using ADMM}
    
     \vspace*{-0.75cm}