What can I do/What is the best practice when frame content is larger than frame size?

Question

\documentclass{beamer}
\usepackage{tikz}
\usepackage{amsmath}
\usetheme{Madrid}
\logo{%
  \includegraphics[width=1cm,height=1.5cm,keepaspectratio]{example-image-a}%
  \hspace{\dimexpr\paperwidth-2cm-5pt}%
  \includegraphics[width=1cm,height=1cm,keepaspectratio]{example-image-b}%
}
\begin{document}
\begin{frame}
  \frametitle{Equation}
  \begin{exampleblock}{}
   \[
     \min_{\mu_{i},c_{i},w_{ij},\mathcal{A}}\quad \sum_{i}^{N}\varphi_{i}(\mu_{i}) + \lvert\mathcal{A}\rvert P_{f} + \frac{1}{\eta}\sum_{i = 1}^{N}\sum_{j\in{A}}w_{ij}^{H}w_{ij}
   \]
  \end{exampleblock}
  subject to
  \begin{exampleblock}{}
    \[
      \frac{1}{\mu_{i}- \lambda_{i}} + \frac{1}{c_{i} - \lambda_{i}}\leq\tau_{i}
    \]
    \[
      \lambda_{i} < \mu_{i},\lambda_{i}<c_{i}
  %    4545
  \]
  \[
    c_i{i} \leq B_{i}\log(1+\text{SINR}_{i}(\mathcal{A}))
  \]
  \[
    \sum_{i=1}^{N}w_{ij}^{H}w_{ij}\leq E_{i},\quad \forall i\in \mathcal{N}, \quad \forall j\in \mathcal{L}
  \]
  \end{exampleblock}
  \begin{itemize}
   %symbol's used in the equation meaning
    \item $\varphi_{i}(\mu_{i})$\quad VM $i$'s power consumption
    \item $\mu_{i}$\qquad VM $i$'s computation capacity/service rate/processing rate
    \item $P_{f}$\qquad power consumption active fibre links
    \item $\eta\in(0,1)$\quad ineffficiency coefficient amplifier in RRH
    \item $\mathcal{A}$\qquad set of active RRHs
    \item $w_{ij}\in\mathbb{C}^{k}$\quad transmit beamformer for UE $i$ from RRH $j$
    \item $i\in\mathcal{N}$
    \item $j\in\mathcal{A}$
  \end{itemize}
\end{frame}
\end{document}

Answer 1

There's a lot of wasted space in your slide with centred math taking up the whole width of the slide. I would put the math in one column and the variable list in another column and reduce just the size of the variable list.

With just the columns code, there's some extra vertical space both at the top of the slide and in the first block. I'm not sure where this is coming from. I've added some manual negative space so that the lefthand logo is not covered.

\documentclass{beamer}
\usepackage{tikz}
\usepackage{amsmath}
\usetheme{Madrid}
\logo{%
  \includegraphics[width=1cm,height=1.5cm,keepaspectratio]{example-image-a}%
  \hspace{\dimexpr\paperwidth-2cm-5pt}%
  \includegraphics[width=1cm,height=1cm,keepaspectratio]{example-image-b}%
}
\begin{document}
\begin{frame}
  \frametitle{Equation}
\vspace*{-2.5\baselineskip}
\begin{columns}[t]
\begin{column}{.62\linewidth}
  \begin{exampleblock}{}%
   \vspace*{-\baselineskip}\[
     \min_{\mu_{i},c_{i},w_{ij},\mathcal{A}}\quad \sum_{i}^{N}\varphi_{i}(\mu_{i}) + \lvert\mathcal{A}\rvert P_{f} + \frac{1}{\eta}\sum_{i = 1}^{N}\sum_{j\in{A}}w_{ij}^{H}w_{ij}
   \]
  \end{exampleblock}
  subject to
  \begin{exampleblock}{}%
    \[
      \frac{1}{\mu_{i}- \lambda_{i}} + \frac{1}{c_{i} - \lambda_{i}}\leq\tau_{i}
    \]
    \[
      \lambda_{i} < \mu_{i},\lambda_{i}<c_{i}
  %    4545
  \]
  \[
    c_i{i} \leq B_{i}\log(1+\text{SINR}_{i}(\mathcal{A}))
  \]
  \[
    \sum_{i=1}^{N}w_{ij}^{H}w_{ij}\leq E_{i},\quad \forall i\in \mathcal{N}, \quad \forall j\in \mathcal{L}
  \]
  \end{exampleblock}
\end{column}
\begin{column}{.38\linewidth}
\footnotesize\raggedright
  \begin{itemize}
   %symbol's used in the equation meaning
    \item $\varphi_{i}(\mu_{i})$\quad VM $i$'s power consumption
    \item $\mu_{i}$\qquad VM $i$'s computation capacity/service rate/processing rate
    \item $P_{f}$\qquad power consumption active fibre links
    \item $\eta\in(0,1)$\quad ineffficiency coefficient amplifier in RRH
    \item $\mathcal{A}$\qquad set of active RRHs
    \item $w_{ij}\in\mathbb{C}^{k}$\quad transmit beamformer for UE $i$ from RRH $j$
    \item $i\in\mathcal{N}$
    \item $j\in\mathcal{A}$
  \end{itemize}
\end{column}
\end{columns}
\end{frame}
\end{document}