How to number rows in an array environment that is contained in an align environment

Question

I am trying to typeset a multiple line optimization problem in LaTeX.

I have had a lot of difficulty using the align and alignat environments to get things to align properly.

I recently managed to find a solution that can get proper alignment by using an array environment inside of an align environment. A sample of this code looks like

\documentclass{article}
\usepackage{amsmath,array}
\begin{document}
    \begin{align}
    \centering
    \begin{array}{>{\displaystyle}l>{\displaystyle}c>{\displaystyle\hspace{0.5cm}}l}
    \min_{\bm{\alpha},\bm{\beta},\bm{\gamma},\lambdab} & \frac{1}{N}\sum_{i=1}^{N}\alpha_i + C_0\sum_{j=1}^{P}\beta_j + C_1\sum_{j=1}^{P}{\gamma_j} & \\
    \textrm{s.t.} & & \\
    & -M\alpha_i + \varepsilon \leq y_i \mathbf{x}_i^T \lambdab \leq M(1-\alpha_i) + \varepsilon & i= 1\ldots N \\
    & -M\alpha_i + \varepsilon \leq y_i \mathbf{x}_i^T \lambdab \leq M(1-\alpha_i) + \varepsilon & i= 1\ldots N 
    \end{array}
    \end{align}
\end{document}
\documentclass{article}

My issue here is that I cannot number each of the rows inside the array environment. I am wondering if anyone knows a way to number / label these rows?

I realize that there have been several solutions that have been posted here, but in many cases the fix seems involve defining my own numbering system within the equations. I would rather try to avoid this since I am using numbering throughout the remainder of the paper, and I think that this would produce a conflict (I could be wrong).

If not, I would be happy with any solution that can generically produce this type of alignment (i.e. 3 columns, 1 left centered; 1 middle centered; 1 left centered).

Answer 1

I would suggest you use alignat instead

\documentclass{article}

\usepackage{amsmath,array,bm}

\begin{document}

\begin{alignat}{3}
  &\min_{\bm{\alpha},\bm{\beta},\bm{\gamma},\lambda} \quad&&
  \frac{1}{N}\sum_{i=1}^{N}\alpha_i + C_0\sum_{j=1}^{P}\beta_j +
  C_1\sum_{j=1}^{P}{\gamma_j} \\ 
  &\textrm{s.t.} \notag \\
  &&& -M\alpha_i + \varepsilon \leq y_i \mathbf{x}_i^T \lambda \leq
  M(1-\alpha_i) + \varepsilon &\quad i&= 1\ldots N \\ 
  &&& -M\alpha_i + \varepsilon \leq y_i \mathbf{x}_i^T \lambda \leq
  M(1-\alpha_i) + \varepsilon & i&= 1\ldots N  
\end{alignat}

\end{document}

The alignment here is {rlrlrl}. An alternative much closer to your original coding is the equationarray environment from eqnarray. Here is an example, but I would prefer to stick to amsmath environments:

\documentclass{article}

\usepackage{amsmath,array,eqnarray,bm}

\begin{document}

\begin{equationarray}{lc>{\hspace{0.5cm}}l}
  \min_{\bm{\alpha},\bm{\beta},\bm{\gamma},\lambda} & \frac{1}{N}\sum_{i=1}^{N}\alpha_i + C_0\sum_{j=1}^{P}\beta_j + C_1\sum_{j=1}^{P}{\gamma_j} & \\
  \textrm{s.t.} & & \notag\\
  & -M\alpha_i + \varepsilon \leq y_i \mathbf{x}_i^T \lambda \leq
  M(1-\alpha_i) + \varepsilon & i= 1\ldots N \\ 
  & -M\alpha_i + \varepsilon \leq y_i \mathbf{x}_i^T \lambda \leq
  M(1-\alpha_i) + \varepsilon & i= 1\ldots N  
\end{equationarray}

\end{document}