[Tex/LaTex] Ignoring alignment for certain lines in an alignat environment

alignmath-mode

I am having trouble typesetting an optimization problem, and would like to know how to ignore the alignment for a certain line in an alignat environment.

I've currently typeset the optimization problem as:

\begin{alignat}{4}
\centering
\min_{\lambda} \quad & \frac{1}{N} \sum_{i = 1}^N{\alpha_i} & + & C_0 \sum_{i = 1}^N{\beta_i} & + & C_1 \sum_{i = 1} ^N{\gamma_i} \\
s.t. \quad & -M\alpha + \epsilon & \leq & \lambda^T X y & \leq & M(1-\alpha) + \epsilon \\ 
     & -\beta \bar{\lambda}  & \leq &  \lambda & \leq & \beta \bar{\lambda} \\ 
     &-\gamma & \leq & \lambda & \leq & \gamma \\ 
     & \lambda \in \mathbb{Z}^P & \quad & \alpha \in \{0,1\}^N  &\quad & \beta, \gamma \in \{0,1\}^P 
\end{alignat}

However this runs into issues since the bottom line causes weird spacing.

I would appreciate any formulations that can make this mess legible in some way… That said, I think that I can get around this problem if I can just tell the alignat environment to ignore the last line, and also center the contents between each of the & signs.

Best Answer

I wouldn't try aligning the inequalities: the formulas are too different from each other. Here's a possibility:

\documentclass{article}
\usepackage{amsmath,amssymb}
\begin{document}
\begin{gather}
\min_{\lambda}
  \,\frac{1}{N} \sum_{i=1}^N{\alpha_i} +
   C_0 \sum_{i=1}^N{\beta_i} +
   C_1 \sum_{i=1} ^N{\gamma_i}
\\
\begin{align}
\makebox[0pt][r]{s.t.\quad}
  &{-}M\alpha + \epsilon \leq \lambda^T X y \leq M(1-\alpha) + \epsilon \\[1ex]
  &{-}\beta \bar{\lambda} \leq \lambda \leq \beta \bar{\lambda} \\[1ex]
  &{-}\gamma \leq \lambda \leq \gamma \\[1ex]
  &\lambda \in \mathbb{Z}^P,\qquad
   \alpha \in \{0,1\}^N, \qquad  \beta, \gamma \in \{0,1\}^P
\end{align}
\end{gather}
\end{document}

It's necessary to use {-} because otherwise the minus sign would be detached from the symbol it refers to.

enter image description here

Related Solutions

[Tex/LaTex] Centering column in alignat environment

At its heart the alignat environment is built on TeX's \halign. In that environment you can ignore the formatting specifications for a given column by issuing \omit. Thus writing

\omit\hfill text \hfill

will give you a centered column of text, since the column specification not only included the left/right alignment but also that the meterial is set as mathematics. It is probably best to create a separate command to provide this construction, which may then be used anywhere in an alignat, align or similar enviroment, at the beginning of a cell:

Sample output

\documentclass{article}

\usepackage{amsmath}

\newcommand{\ditto}{{''}}
\newcommand{\ccol}[1]{\omit\hfill #1\hfill}

\begin{document}

\begin{alignat*}{3}
  &E&\quad&\ccol{par}&\quad&\Sigma,\\
  &\Psi&&\ccol{\ditto}&&\frac{\epsilon V}{1+4\pi\epsilon F},\\
  &\Psi&&\ccol{\ditto}&&\frac{(1+4\pi\epsilon F)^2}{\epsilon}.
\end{alignat*}

\begin{align}
  E &= mc^2\\
  F &\ccol{is another quantity}\\
  G &= u^2 + v^2 - w^2 + x^2 - y^2 + z^2
\end{align}

\end{document}

Sould you wish to span multiple columns the relevant command is \multispan, e.g. \multispan{3}\hfill text \hfill will place text spread over three columns and centered.

Alternatively, as Harish Kumar suggests you can use array or tabular:

Second sample

\documentclass{article}

\usepackage{amsmath}

\newcommand{\ditto}{{''}}

\begin{document}

\begin{equation*}
  \begin{array}{r@{\quad}c@{\quad}l}
  E&\mathrm{par}&\Sigma,\\
  \Psi&\mathrm{\ditto}&\displaystyle\frac{\epsilon V}{1+4\pi\epsilon F},\\
  \Psi&\mathrm{\ditto}&\displaystyle\frac{(1+4\pi\epsilon F)^2}{\epsilon}.
  \end{array}
\end{equation*}

\begin{center}
  \begin{tabular}{r@{\quad}c@{\quad}l}
    \( E \)&par&\( \Sigma, \)\\
    \( \Psi \)&\ditto&\( \displaystyle\frac{\epsilon V}{1+4\pi\epsilon F}, \)\\
    \( \Psi \)&\ditto&\( \displaystyle\frac{(1+4\pi\epsilon F)^2}{\epsilon}. \)
  \end{tabular}
\end{center}
\end{document}

However, the default line spacing from alignat is better and you don't need to worry about adjusting the math styles.

[Tex/LaTex] alignat inside align environment

the easiest fix is to use your second attempt, but instead of just \phantom{+}, surround the plus sign by empty groups to force the correct spacing:

\begin{equation}
  \begin{dcases}
    \label{eq:115}
    {\begin{aligned}
        U(x,y,z,t)=\int\frac{x'-x}{r^3}[&\phantom{{}+{}}(x'-x)u(x',y',z',t)\\
                                        &+(y'-y)v(x',y',z',t)\\
                                        &+(z'-z)w(x',y',z',t)]d\omega',
      \end{aligned}}\\
    V(x,y,z,t)=\ldots\ldots,\quad W(x,y,z,t)=\ldots\ldots
  \end{dcases}
\end{equation}

for your first attempt, alignat* isn't meant to be embedded. instead, alignedat (defined by mathtools) is appropriate. but you will still need to add empty groups around plus signs, in this case, the two that are between the ampersands:

\begin{equation}
  \label{eq:115}
  \left\{
    \begin{aligned}
      \begin{alignedat}{2}
        &U(x,y,z,t)=\int\frac{x'-x}{r^3}[& &(x'-x)u(x',y',z',t)\\
        &                                &{}+{}&(y'-y)v(x',y',z',t)\\
        &                                &{}+{}&(z'-z)w(x',y',z',t)]d\omega',
      \end{alignedat}\\
        V(x,y,z,t)=.....,\quad W(x,y,z,t)=..... .
    \end{aligned}
  \right.
\end{equation}

output of code input

i'm also not sure why you didn't use cases, but that's a niggle.

Best Answer

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[Tex/LaTex] Centering column in alignat environment

[Tex/LaTex] alignat inside align environment

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