Align objective value variable

Question

Z(p) = \begin{mini}|l|
{x}{c^T x}{}{}
\addConstraint{Ax}{\geq b}
\addConstraint{Dx}{\geq d}
\addConstraint{x}{\in \mathbb{Z}}
\end{mini}

How do I get the Z(p) to be aligned properly?

Answer 1

By using mini! and the optidef package examples it seems this is a result being sought:

\documentclass[12pt]{article}
\usepackage{optidef}
\begin{document}
\begin{mini!}|s|[2]<b>
{x}{c^T , x}
{\label{eq:Example1}}
{Z(p) =}
\addConstraint{Ax}{\geq b}
\addConstraint{Dx}{\geq d}
\addConstraint{x}{\in \mathbb{Z}}
\end{mini!}
\end{document}

which gives:

Answer 2

If you want to use an AMS-related structure (with or without equation numbering):

\documentclass{article}
\usepackage{amsmath,amsfonts}
\begin{document}
[
  Z(p) = \begin{aligned}[t]
         \min_x~ & c^T x \
    \text{s.t.}~ & \begin{aligned}[t]
      Ax &\geq b, \
      Dx &\geq d, \
       x &\in \mathbb{Z}
    \end{aligned}
  \end{aligned}
]
\begin{subequations}
  \begin{alignat}{2}
    Z(p) ={}&      \min_x \rlap{~$c^T x$} \
            & \text{s.t.} & Ax &\leq b, \
            &             & Dx &\leq d, \
            &             &  x &\in \mathbb{Z}
  \end{alignat}
\end{subequations}
\end{document}