11

I have this expression involving minimisation. How do I split it over two lines? The problem is \min seems to be separated from the objective function. breqn does not seem to work, as this is not an equation.

$$\min_{\substack{A,B,\\ 0\le A\le T \\ D+X+W-S\ge 0}}\bigg(I+X+W-E,-(X+k(A-B))\bigg)$$
lockstep
  • 250,273
Bravo
  • 723
  • is \min\bigg(I+X+W-E,-(X+k(A-B))\bigg)_{\substack{A,B,\ 0\le A\le T \ D+X+W-S\ge 0}} acceptable? – Tom Bombadil May 25 '12 at 10:19
  • I have never seen an opti. problem posed like that. But in case, I am constrained in horizontal space, so that doesn't work. – Bravo May 25 '12 at 10:40
  • Why do you have a comma in the function to be minimized? – percusse May 25 '12 at 11:08
  • @percusse: It is multivalued objective function - two functions minimised simultaneously over common constraint space. – Bravo May 25 '12 at 13:03
  • @Shyam Sorry for my ignorance about it. I was suspecting that but I couldn't understand how you can do that without a functional e.g. how do you order (1,2) and (2,1). I know it's not related to TeX at all but just out of curiosity :) You can also bash me in our chat room if you feel like it – percusse May 25 '12 at 13:18

3 Answers3

11

If you need to break up the conditions of the minimization problem across two or more lines, the following will work:

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{equation*}
  \min_{\substack{A,B\\ 0\le A\le T \\ 
     D+X+W-S\ge 0}}
  \Bigl(I+X+W-E-\bigl(X+k(A-B)\bigr)\Bigr)
\end{equation*}
\end{document}

enter image description here

If you want the minimization conditions to be spread over just two lines, replace the first \\ with ;\ and you'd get:

enter image description here

Addendum, posted after receiving a clarification from the OP: If, rather, the objective is to break up the argument of the minimization problem (I must confess I'd overlooked the comma in the earlier MWEs), the following should be of interest:

\documentclass{article}
\usepackage{mathtools}
\setlength\textwidth{2in} % simulate a narrow column
\begin{document}
\begin{multline*}
  \min_{\mathclap{\substack{A,B\\ 0\le A\le T \\ D+X+W-S\ge 0}}}
     \big(I+X+W-E,\\[-5ex]
     X+k(A-B)\big)
\end{multline*}
\end{document}

enter image description here

Mico
  • 506,678
  • With the first way, one can also insert a negative space before the objective function, so as to shift it nearer "min". Avoiding the parentheses' growth would render this quite nicely. – egreg May 25 '12 at 10:37
  • Thanks @Mico, but this is not what I am looking for. I have a 1-column space in a 2-column write-up. Is it possible to split the two obj. functions appropriately? The constraints are not the problem, as I have enough vertical space. – Bravo May 25 '12 at 10:39
  • This is nice, but the matrix is elevated compared to the min and that makes it awkward. – Bravo May 25 '12 at 13:06
  • 1
    OK, I made another modification -- now using the multline environment rather than the pmatrix environment. Hope this meets your needs. – Mico May 25 '12 at 14:15
  • Thanks a lot for your efforts, @Mico. This is exactly what I had wanted :) – Bravo May 25 '12 at 14:48
  • The mathclap in there is kind of dangerous though. Here it works, but if you take a larger brace (e.g. \bigg), it might protrude into the text set under min. Is there actually a way to fix something like that? For example by pushing the text down a bit? – mSSM May 25 '12 at 21:29
  • @mSSM -- Sadly (or happily?!!), very few TeX macros are completely safe. :-) I deliberately chose \big rather than \Big as the modifier for the opening parenthesis so that there wouldn't be a clash. If you did need to move the first line ("A,B") down a bit, you could do so by inserting something like \\[1ex] (or whatever amount is required) right before A,B; of course, you'd then have to increase the negative adjustment after -E, by the same amount -- in the present example from \\[-5ex] to \\[-6ex]. – Mico May 25 '12 at 21:50
  • @Mico --- right, thanks. That's the easiest solution. I recently ran into a similar problem, and messing with raiseboxes and vphantoms was rather messy... :) – mSSM May 26 '12 at 07:00
5

Refining Mico's answer according to your comment: You can use an alignat environment to set the equation in two rows and two columns. Each row's third & defines the alignment position, while \notag and \\[-2em] ensure that (1) there is just one equation number and (2) that in spite of the height of the cell containing min, the lines are not overly spaced.

enter image description here

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{alignat}{2}
  &\min_{\substack{A,B\\ 0\le A\le T \\ 
     D+X+W-S\ge 0}}
     &\bigg(I+X &+W-E,\notag\\[-2em]
  &  &          &-(X+k(A-B))\bigg)
\end{alignat}
\end{document}

 

Addendum:

As @mSSM pointed out in a comment, the equation environment is superior to alignat when it comes to determining the space between the equation and surrounding paragraphs. It may therefore be desirable to use the alignedat (note the ed) subsidiary environment inside an equation environment, as depicted in the second figure below. Note the centered placement of the equation number.

enter image description here

 

enter image description here

The second figure's code:

\begin{equation}
\begin{alignedat}{2}
  &\min_{\substack{A,B\\ 0\le A\le T \\ 
     D+X+W-S\ge 0}}
     &\bigg(I+X &+W-E,\\[-2em]
  &  &          &-(X+k(A-B))\bigg)
\end{alignedat}
\end{equation}
dgs
  • 2,741
  • If you want to typeset only one equation, it is better to use \begin{alignedat} inside a \begin{equation} environment. Also, the \qquad can be replaced by a simple {}.

    EDIT: Geez this was ugly; removed my rewrite, because it looked messed up as a comment.

     – mSSM May 25 '12 at 12:10
  • Ah, sure. Initially I had the second row not aligned but indented, that's where the \qquad came from. Why is it superior to place alignedat inside an equation? – dgs May 25 '12 at 12:31
  • For one, it makes more sense. :) If you only typeset one equation (even if it happens to be on several lines), then you shouldn't use an environment which is made for typesetting several equations.

    Also, you don't have to put \notags everywhere (less clutter).

    And last but not least, the equation environment is "more powerful" than align: http://tex.stackexchange.com/a/325/6993

     – mSSM May 25 '12 at 12:52
  • Thanks @dgs, this seems the closest to what I had hoped for. Will wait for some more comments/answers before accepting. – Bravo May 25 '12 at 13:07
  • @mSSM Thanks for pointing me at the spacing issue; I've wondered about that a few times but wasn't aware it's a feature. – dgs May 25 '12 at 14:12
2

If you are having freedom to change styles, my suggestion is to reduce cluttering parameters inside the main equation. Here are the different possibilities:

\documentclass{article}
\usepackage{amsmath}
%
\begin{document}
 \textbf{version - 1:}
\[\min_{\substack{A,B;\ 0\le A\le T \\ D+X+W-S\ge 0}}\bigg(I+X+W-E,-(X+k(A-B))\bigg)\]

\textbf{version - 2:}
\[\min_{\substack{A,B}}\bigg(I+X+W-E,-\big(X+k(A-B)\big)\bigg) \qquad \text{ subject to } 0\le A\le T \text{  and  } D+X+W-S\ge 0\]

\textbf{version - 3:}
\[\min_{\substack{A,B}}\bigg(I+X+W-E,-\big(X+k(A-B)\big)\bigg) \]
subject to
\[0\le A\le T\]
\[D+X+W-S\ge 0\].
\end{document}

enter image description here

You may try to split parameters more meaningfully and the equation becomes more readable IMO.