split large formula in align

Question

I have a large formula in align:

\begin{align}
\overline{r}_D(n_D) = \begin{cases}
r_D(n_D)  & \textrm{ if } r_D(n_D)  < b_{min} \\
\max\{b_{min} , \max \{b_{l-f(\rho_E)} \mid b_l \leq r_D(n_D), \; 1\leq l \leq m\}\}& \textrm{otherwise} 
\end{cases}
\nonumber
\end{align}

And it looks like this:

It overlaps with the the column on the right. How can I fix it ?

EDIT:

Here is the compilable script:

\documentclass[10pt,a4paper,twocolumn]{IEEEtran}

\usepackage{graphicx,amssymb,amsmath,amsfonts,mathtools, bm}


\begin{document}


Postremo ad id indignitatis est ventum, ut cum peregrini ob formidatam haut ita dudum alimentorum inopiam pellerentur ab urbe praecipites, sectatoribus disciplinarum liberalium inpendio paucis sine respiratione ulla extrusis, tenerentur minimarum adseclae veri, quique id simularunt ad tempus.


\begin{align}
\overline{r}_D(\vec{n}) = \begin{cases}
r_D(\vec{n})  & \textrm{ if } r_D(\vec{n})  < b_{min} \\
\max\{b_{min} , \max \{b_{l-f(\rho_E)} \mid b_l \leq r_D(\vec{n}), \; 1\leq l \leq m\}\}& \textrm{otherwise} 
\end{cases}
\nonumber
\end{align}

Postremo ad id indignitatis est ventum, ut cum peregrini ob formidatam haut ita dudum alimentorum inopiam pellerentur ab urbe praecipites, sectatoribus disciplinarum liberalium inpendio paucis sine respiratione ulla extrusis, tenerentur minimarum adseclae veri, quique id simularunt ad tempus, et tria milia saltatricum ne interpellata quidem cum choris totidemque remanerent magistris.


\end{document}

Answer 1

I would suggest using a temporary variable

\documentclass{amsart}

\begin{document}

Text text text text text text text text text text text text text text
text text text text text text text text text text text text text text
text text text text text text text text text text text text text text
\begin{align}
  {r}_D(n_D)
  =
  \begin{cases}
    r_D(n_D),  & \textrm{ if } r_D(n_D)  < b_{\min}, \\
    \max\{b_{\min},c\},& \textrm{otherwise},
  \end{cases}
\nonumber
\end{align}
where
\( c = \max\{ b_{\ell-f(\rho_E)} \mid b_\ell \leq r_D(n_D), \; 1\leq
\ell \leq m \} \).

\end{document}

Answer 2

You can move “otherwise” to another line, adding some vertical space for better clarity.

\documentclass{article}
\usepackage{amsmath}

\usepackage{lipsum} % for mock text

\begin{document}

\lipsum*[1][1-3]
\begin{equation*}
\overline{r}_D(n_D) =
\begin{cases}
\begin{alignedat}{2}
&r_D(n_D) && \text{if $r_D(n_D)  < b_{\min}$} \\[2ex]
&\!\max\{b_{\min}, \max \{b_{l-f(\rho_E)} \mid b_l \leq r_D(n_D), 1 \leq l &&\leq m\}\} \\
 &&& \text{otherwise}
\end{alignedat}
\end{cases}
\end{equation*}
\lipsum*[2]

\end{document}

For two-column output, you need some more. Something like

\max \{b_{l-f(\rho_E)} \mid b_l \leq r_D(n_D), 1 \leq l \leq m\}

should be given a name; choose what you like more, here I use B(n_D,m).

\documentclass[a4paper]{IEEEtran}
\usepackage{amsmath}
\usepackage{newtxtext,newtxmath}

\usepackage{lipsum} % for mock text

\begin{document}

\lipsum*[1][1-3]
\begin{align*}
&\overline{r}_D(n_D) =
\begin{cases}
r_D(n_D) & \text{if $r_D(n_D)  < b_{\min}$,} \\
\max\{b_{\min}, B(n_D,m)\}& \text{otherwise,}
\end{cases}
\\
&B(n_D,m)=\max \{b_{l-f(\rho_E)} \mid b_l \leq r_D(n_D), 1 \leq l \leq m\}.
\end{align*}
\lipsum*[2][1-3]
\lipsum[4-9]

\end{document}

Note I used newtxtext and newtxmath to avoid (horrible) formulas in Computer Modern along with Times for text.

Answer 3

You can write this equation smaller by help of macro \medmath{...} from the package nccmath:

(red lines indicate text borders)

\documentclass{amsart}
\usepackage{nccmath}

\usepackage{lipsum}
\begin{document}
\lipsum[66]
\begin{align*}
    \medmath{
\overline{r}_D(n_D) = \begin{cases}
r_D(n_D)  
    & \text{ if } r_D(n_D)  < b_{\min} \\
\max\bigl\{b_{\min}, \max\{b_{l-f(\rho_E)} \mid b_l \leq r_D(n_D), \; 1\leq l \leq m\}\bigr\}
    & \text{otherwise}
\end{cases}
            }
\end{align*}
\end{document}

Edit: After your editing of your question only answer of Andrew Swann (+1) can solve your problem. To his solution (and your new MWE) I can only add some off-topic remarks (see comments in code below):

\documentclass[10pt,a4paper]{IEEEtran} % it is default twocolumn
\usepackage{amssymb,    % load amsfonts too
            mathtools,  % it is supersede of the amsmath, no need to load it (again) 
            bm}
\usepackage{graphicx}

\usepackage{lipsum}

\begin{document}
\lipsum[1]
\begin{align*}          % no numbered
\overline{r}_D(n_D) = \begin{cases}
r_D(n_D)  
    & \text{ if } r_D(n_D)  < b_{\min} \\
\max\bigl\{b_{\min}, c_{\max}\bigr\}
    & \text{otherwise}
\end{cases}
\end{align*}
where $c_{max}=\max\{b_{l-f(\rho_E)} \mid b_l \leq r_D(n_D), \; 1\leq l \leq m\}$. 

\lipsum[2-7]
\end{document}

which gives: