[Tex/LaTex] A vertical line between an \fbox and a minipage

Question

I use a template of beamer. In a frame, there is a \fbox on the left and a minipage on the right. But I found it very ugly. So I imagine that it would be nicer if I add a blue vertical line here. Since the main color of the template is blue.

For the .sty files, please download at http://www.ist.tugraz.at/staff/weiglhofer/misc/tugrazposter/

\documentclass[final,hyperref={pdfpagelabels=false}]{beamer} 

\mode<presentation> {  
  \usetheme{TUGraz}    
}
\usepackage{tikz}
\usepackage{pgflibraryshapes}
\usetikzlibrary{arrows}
\usetikzlibrary{shapes}
\usetikzlibrary{automata}
\tikzstyle{model_node}=[circle,draw=black,fill=tuggreen!50,minimum size=50pt]
\tikzstyle{tool}=[draw,double,rounded corners,inner sep=10pt]
\tikzstyle{aut_node}=[circle,draw=black,fill=black,inner sep=0pt,minimum size=7pt,font=\footnotesize]

\usefonttheme[onlymath]{serif}
\boldmath
\usepackage[orientation=portrait,size=a0,scale=1.4,debug]{beamerposter}                       


\begin{document}


\begin{block}{Primal Dual Algorithm{\color{block title.bg}p}}

\fbox{
\begin{minipage}[c]{0.48\textwidth}%
$\bullet$ Initialization: $\tau\sigma\le\frac{1}{\norm{K}^2}$,$\theta\in\sbra{0,1}$,$(x^0,y^0)\in X\times Y$,$\overline{x}^0 = x^0, \lambda \in \mathbb{R}$

$\bullet$ Iterations $n\ge 0$: Update $x^n, y^n$ as follows,
\begin{align*}
   y^{n+1}&=(I+ \sigma \partial F^*)^{-1}(y^n+\sigma K \overline{x}^n)  \\
   x^{n+1}&=(I+\tau \lambda\partial G)^{-1}({x}^n-\tau K^*y^{n+1})   \\
      \overline{x}^{n+1} &= x^{n+1}+\theta (x^{n+1}-x^{n})
\end{align*}
\end{minipage}
}
\hfill 
\begin{minipage}{0.48\textwidth}
\centering
Online Primal-dual Algorithm:
\begin{equation*}
  \left\{
   \begin{array}{rl}
\widetilde{L}^{n+1}&=\frac{\avg{K(x^n-x^{n-1}),y^{n+1}-y^n}}{\norm{x^{n-1}-x^n}\norm{y^{n+1}-y^n}}\\
   L^{n+1}&=\max\lbra{L^n,\widetilde{L}^{n+1}}\\
    \tau^{n+1}&=\frac{a}{{L^{n+1}}}, \sigma^{n+2}=\frac{1}{a{L^{n+1}}} \\
\end{array}
  \right.
\end{equation*}
 \end{minipage}




\end{block}


\end{document}

Answer 1

Using a minipage on the right will push the object too far away.

Here's a possibility, notice how the rule is obtained with

{\color{red}\vrule}

Code follows; adjust the spacings to suit.

\documentclass[final,hyperref={pdfpagelabels=false}]{beamer} 

%\mode<presentation> {  
%  \usetheme{TUGraz}    
%}

\usepackage{tikz}
\usepackage{pgflibraryshapes}
\usetikzlibrary{arrows}
\usetikzlibrary{shapes}
\usetikzlibrary{automata}
\tikzstyle{model_node}=[circle,draw=black,fill=tuggreen!50,minimum size=50pt]
\tikzstyle{tool}=[draw,double,rounded corners,inner sep=10pt]
\tikzstyle{aut_node}=[circle,draw=black,fill=black,inner sep=0pt,minimum size=7pt,font=\footnotesize]

\usefonttheme[onlymath]{serif}
\boldmath
\usepackage[orientation=portrait,size=a0,scale=1.4,debug]{beamerposter}                       

\newcommand{\norm}[1]{\|#1\|}
\newcommand{\lbra}[1]{?#1?}
\newcommand{\sbra}[1]{?#1?}
\newcommand{\avg}[1]{?#1?}

\begin{document}

\vspace*{1cm}

\begin{block}{Primal Dual Algorithm{\color{block title.bg}p}}
\centering
\fbox{%
  \begin{minipage}[c]{0.48\textwidth}%
  $\bullet$ Initialization: $\tau\sigma\le\frac{1}{\norm{K}^2}$,$\theta\in\sbra{0,1}$,$(x^0,y^0)\in X\times Y$,$\overline{x}^0 = x^0, \lambda \in \mathbb{R}$

  $\bullet$ Iterations $n\ge 0$: Update $x^n, y^n$ as follows,
  \begin{align*}
   y^{n+1}&=(I+ \sigma \partial F^*)^{-1}(y^n+\sigma K \overline{x}^n)  \\
   x^{n+1}&=(I+\tau \lambda\partial G)^{-1}({x}^n-\tau K^*y^{n+1})   \\
      \overline{x}^{n+1} &= x^{n+1}+\theta (x^{n+1}-x^{n})
  \end{align*}
  \end{minipage}%
}
\qquad{\color{red}\vrule}\qquad
\begin{tabular}{@{}l@{}}
   Online Primal-dual Algorithm:\\
   $\displaystyle
   \left\{
   \begin{array}{rl}
     \widetilde{L}^{n+1}&=\frac{\avg{K(x^n-x^{n-1}),y^{n+1}-y^n}}{\norm{x^{n-1}-x^n}\norm{y^{n+1}-y^n}}\\
     L^{n+1}&=\max\lbra{L^n,\widetilde{L}^{n+1}}\\
     \tau^{n+1}&=\frac{a}{{L^{n+1}}}, \sigma^{n+2}=\frac{1}{a{L^{n+1}}} \\
   \end{array}
  \right.
  $
\end{tabular}\hspace*{\fill}

\end{block}

\end{document}