diff --git a/latex/presentations/final/sections/decoding_algorithms.tex b/latex/presentations/final/sections/decoding_algorithms.tex index 327d2e0..2fe1065 100644 --- a/latex/presentations/final/sections/decoding_algorithms.tex +++ b/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}