샘플 코드

\documentclass[12pt, a4paper, papersize, dvipdfmx]{jsarticle}

% ---- Preamble -------------------------------------------------------------- %
% -------- Packages ------------------------------------------------------ %
% AMS
\usepackage{amsmath}

% Ref
\usepackage{nameref}

% -------- Environments -------------------------------------------------- %
% New Environments
\newcounter{mpproblem}[section]
\renewcommand{\thempproblem}{\thesection.\arabic{mpproblem}}
\makeatletter
\newenvironment{mpproblem}[1]%
{%
    \protected@edef\@currentlabelname{#1}%
    \par\vspace{\baselineskip}\noindent%
    \ifx#1\empty %
    \else \refstepcounter{mpproblem}$($#1$)$ %
    \fi%
    \hfill%
    $\left|%
    \hfill%
    \hspace{0.00\textwidth}%
    \@fleqntrue\@mathmargin\parindent%
    \begin{minipage}{0.86\textwidth}%
    \vspace{-1.0\baselineskip}%
}%
{%
    \end{minipage}%
    \@fleqnfalse%
    \right.$%
    \par\vspace{\baselineskip}\noindent%
    \ignorespacesafterend%
}%
\makeatother
\newcommand{\mpprobref}[1]{$($\nameref{#1}$)$}

\newenvironment{mpproblem*}%
{%
    \begin{mpproblem}{}%
}%
{%
    \end{mpproblem}%
    \ignorespacesafterend%
}



% ---- Text ------------------------------------------------------------------ %
\begin{document}

問題名あり。
%
\begin{mpproblem}{$P$}
\label{mpprob:P}
\begin{alignat}{2}
 &\text{minimize}   & \quad  c^\top x  &        \label{eqn:P_Obj}     \\
 &\text{subject to} & \quad  Ax        &\geq b  \label{eqn:P_Con-Eq}  \\
 &                  & \quad  x         &\geq 0. \label{eqn:P_Con-Non} 
\end{alignat}
\end{mpproblem}

問題名なし。
%
\begin{mpproblem*}
\begin{alignat}{2}
 &\text{minimize}   & \quad f(x)  &        \label{eqn:FG_Obj}    \\
 &\text{subject to} & \quad g(x)  &\leq 0. \label{eqn:FG_Con-Eq} 
\end{alignat}
\end{mpproblem*}

nameref（hyperref）パッケージを使えば、
問題名\mpprobref{mpprob:P}は相互参照可能。

\end{document}