You may want to switch between numbering equations on the left/right and use a gather
to centre content - the alignment in your post seems non-uniform. To achieve some form of alignment around =
, I've used boxes via \eqmakebox[<tag>][<align>]{<stuff>}
. This sets <stuff>
in a box of maximum width across the same <tag>
using the appropriate <align>
ment; l
eft and r
ight in my case.

\documentclass{article}
\usepackage[leqno]{amsmath}
\usepackage{eqparbox}
% https://tex.stackexchange.com/q/193535/5764
\makeatletter
\newcommand{\leqnomode}{\tagsleft@true}
\newcommand{\reqnomode}{\tagsleft@false}
\makeatother
\begin{document}
\reqnomode
\begin{align}
f(x) &= ax^2 + bx + c \\
g(x) &= dx^2 + ex + f
\end{align}
\leqnomode
\begin{gather}
\eqmakebox[LHS][r]{$\min\ f(x)$}
\eqmakebox[RHS][l]{$\displaystyle {}= \sum_{j = 1}^n f_j(x_j)$} \tag{P} \\
\eqmakebox[LHS][r]{$\textup{s.t.}\ g_i(x)$}
\eqmakebox[RHS][l]{$\displaystyle {}= \sum_{j = 1}^n g_{ij}(x_j) \leq b_i,\ i = 1,\dots,m,$} \nonumber \\
x \in X = X_1 \times X_2 \times \dots \times X_n, \nonumber
\end{gather}
\reqnomode
\begin{align}
f(x) &= ax^2 + bx + c \\
g(x) &= dx^2 + ex + f
\end{align}
\end{document}