Splitting long equation in LaTeX

Question

I am having the following equation:

\begin{equation}
         \sum^{n}_{\stackrel{i=1}{(j,i)\in Q}} \left\{ w^{1}_{ijR}+\sum^{m=1}_{\stackrel{(m,i)\in Q}{m\neq j}} \left[ (w^{2}_{ijmR}+w^{2}_{ijm,R-1})  + \sum^{l=1}_{\stackrel{(l,i)\in Q}{i\neq j\neq m}} (w^{3}_{ijmlR}+w^{3}_{ijml,R-1}+w^{3}_{ijml,R-2}) \right]                         \right\}+     \sum^{n}_{\stackrel{j=1}{(l,i)\in Q}} \left\{ w^{1}_{jiR}+ \sum^{m=1}_{\stackrel{(m,j)\in Q}{m\neq i}}         \left[ (w^{2}_{jimR}+w^{2}_{jmi,R-1}) +\sum^{l=1}_{\stackrel{(l,j)\in Q}{m\neq i\neq l}}(w^{3}_{jimlR}+w^{3}_{jmil,R-1}+w^{3}_{jmli,R-2})   \right]  \right\}=1    ~ ~ ~ i=1,...,n  ~ ~ ~ R=1,...,n-1
\end{equation}

How can I split this over three lines??

Answer 1

Here is a solution, if you don't need margin notes, with two variants for the second equation. A small remark: for multiline indices, you should use \substack, not \stackrel which is designed to add something over a relation symbol, so that the two rows use the same font size. I also used smaller delimiters.

\documentclass{article}
\usepackage{geometry}
\usepackage{mathtools}

\begin{document}

\begin{multline}
    \begin{aligned}
          &\smashoperator{ \sumⁿ_{\substack{i=1\\(j,i) ∈ Q}}}\, \Biggl\{ w^{1}_{ijR}+\sum^{m=1}_{\substack{(m,i) ∈ Q\\m ≠ j}} \Biggl[ (w^{2}_{ijmR}+w^{2}_{ijm,R-1}) + \smashoperator{\sum^{l=1}_{\substack{(l,i) ∈ Q\\i ≠ j ≠ m}}} (w^{3}_{ijmlR}+w^{3}_{ijml,R-1}+w^{3}_{ijml,R-2}) \Biggr] \Biggr\} \\
          + & \smashoperator{\sumⁿ_{\substack{j=1\\(l,i) ∈ Q}}} \Biggl\{ w^{1}_{jiR}+ \sum^{m=1}_{\substack{(m,j) ∈ Q\\ m ≠ i}} \Biggl[ (w^{2}_{jimR}+w^{2}_{jmi,R-1}) + \smashoperator{\sum^{l=1}_{\substack{(l,j) ∈ Q\\ m ≠ i ≠ l}}}(w^{3}_{jimlR}+w^{3}_{jmil,R-1}+w^{3}_{jmli,R-2}) \Biggr] \Biggr\}
    \end{aligned} \\
         =1 ,\qquad i=1,...,n,\quad R=1,...,n-1
 \end{multline}\\

 \begin{multline} \smashoperator{\sum^{n}_{\substack{j=1\\ (j,i)\in Q}}} \Biggl\{w^{1}_{ijR}+w^{1}_{ij,R+1}+\smashoperator{\sum^{n}_{\substack{m=1 \\ (m,i)\in Q \\ m\neq j}}} \,\biggl[w^{2}_{ijm,R-1}+w^{2}_{ijmR}+w^{2}_{ijm,R+1} \\[-6ex]
  + \smashoperator{\sum^{n}_{\substack{l=1 \\ (l,i)\in Q \\ i\neq j\neq m}}}(w^{3}_{ijml,R-2}+w^{3}_{ijmlR}+w^{3}_{ijml,R+2}) \biggr] \Biggr\} \leq 1
\end{multline} \\

  \begin{equation}
  \begin{aligned}[b]
  \smashoperator{\sum^{n}_{\substack{j=1\\ (j,i)\in Q}}} \Biggl\{w^{1}_{ijR}+w^{1}_{ij,R+1}+\smashoperator{\sum^{n}_{\substack{m=1 \\ (m,i)\in Q \\ m\neq j}}} \,\biggl[w^{2}_{ijm,R-1} & + w^{2}_{ijmR}+w^{2}_{ijm,R+1} \\[-5.5ex]
  & + \smashoperator{\sum^{n}_{\substack{l=1 \\ (l,i)\in Q \\ i\neq j\neq m}}}(w^{3}_{ijml,R-2}+w^{3}_{ijmlR}+w^{3}_{ijml,R+2}) \biggr] \Biggr\} \leq 1
\end{aligned}
 \end{equation}

\end{document}

Answer 2

• assumed, that the page borders widths are 25mm
• with use of multlined math environment from the mathtools package:

(red lines indicate text bordes)

\documentclass{article}
\usepackage[margin=25mm]{geometry}
\usepackage{mathtools}
%---------------- show page layout. don't use in a real document!
\usepackage{showframe}
\renewcommand\ShowFrameLinethickness{0.15pt}
\renewcommand*\ShowFrameColor{\color{red}}
%---------------------------------------------------------------%

\begin{document}
\begin{equation}
    \begin{multlined}[0.95\hsize]
\sum^{n}_{\stackrel{i=1}{(j,i)\in Q}} 
\left\{ w^{1}_{ijR}+\smashoperator[l]{\sum^{m=1}_{\stackrel{(m,i)\in Q}{m\neq j}}} 
\left[  \Bigl(w^{2}_{ijmR}+w^{2}_{ijm,R-1}\Bigr)  + 
                    \smashoperator[l]{\sum^{l=1}_{\stackrel{(l,i)\in Q}{i\neq j\neq m}}}
        \Bigl(w^{3}_{ijmlR}+w^{3}_{ijml,R-1}+w^{3}_{ijml,R-2} \Bigr)
\right]     
\right\}+  \\   
\sum^{n}_{\stackrel{j=1}{(l,i)\in Q}} 
\left\{ w^{1}_{jiR}+ \smashoperator[l]{\sum^{m=1}_{\stackrel{(m,j)\in Q}{m\neq i}}}         
\left[  \Bigl(w^{2}_{jimR}+w^{2}_{jmi,R-1}\Bigr) +
                    \smashoperator[l]{\sum^{l=1}_{\stackrel{(l,j)\in Q}{m\neq i\neq l}}}
        \Bigl(w^{3}_{jimlR}+w^{3}_{jmil,R-1}+w^{3}_{jmli,R-2}\Bigr)
\right]  
\right\}=1,\\
 i=1,...,n ;\ R=1,...,n-1
    \end{multlined}
\end{equation}
\end{document}