equations in tikz commutative diagram

Question

This question had good answers, here:

equation label within commutative diagram

and I thank everyone again.

But the text is very sensitive to changes, so when I try to change what people suggested, I get error messages.

So I created the smallest possible MWE:

\documentclass{article}
\usepackage{amsmath}
\usepackage{tikz}

\usepackage{hyperref, longtable, tabu, booktabs}
\usetikzlibrary{arrows.meta,shapes.arrows}

\usepackage{tikz-cd}


\begin{document}


    \begin{figure}[h]
        \begin{equation*} \label{eqn-commutative}
        \begin{tikzcd}[row sep=huge, column sep=width("bbbbbbbbbbbbbbbbbbbbbbb")]  
        A    \arrow[r,  "\qquad \qquad \qquad \quad  \mathrm{some \; text \; here} \hspace{3cm}"]  
        \arrow[d,   "\mathrm{some \, down \, text \, here}"  swap]  &     \arrow[d,  "\mathrm{some \, down \, text \, here}" ] B  \\

        C        & D    \arrow[l, "\qquad \qquad \qquad \quad  \mathrm{some \; text \; here} \hspace{3cm}" ] \\

        \end{tikzcd} 
        \end{equation*} 
        \vspace{-1.5cm} 
        \caption{Figure caption here}  
        \label{figure-commutative} 
    \end{figure}

In place of the "A" I would like the following: 

\begin{equation} \label{eq:1} 
\left\{\begin{array}{rl}
\sup & c^T x  \\
s.t.   & Ax \leq b.
\end{array} \right. 
\end{equation} 

with equation label adjusted to left.

In place of the "B" I would like the following:

\begin{equation} \label{eq:2} 
\left\{\begin{array}{rl}
\sup & f^T x  \\
s.t.   & Dx \leq e.
\end{array} \right. 
\end{equation} 

with equation label adjusted to left.

Then I would like to reference \eqref{eq:1} and \eqref{eq:2} here. 

\end{document}

Answer 1

I'd define a suitable command for this. Note that you don't have to guess the width of the single big piece.

\documentclass{article}
\usepackage{amsmath}
\usepackage{tikz-cd}

\makeatletter
\newcommand{\nodeequation}[1]{%
  \let\label\ltx@label
  \refstepcounter{equation}%
  (\theequation)%
  \quad#1%
}
\makeatother

\begin{document}
\begin{equation*}
\begin{tikzcd}[row sep=4em,column sep=10em,ampersand replacement=\&]
  \nodeequation{
    \label{eq:1}
    \begin{cases}
    \begin{alignedat}{2}
    &\sup          &\quad& c^T x  \\
    &\,\text{s.t.} &\quad& Ax \leq b.
    \end{alignedat}
    \end{cases}
  } 
  \arrow[r,"\text{some text here}"] \arrow[d,swap,"\text{some text here}"] \&
  \nodeequation{
    \label{eq:2}
    \begin{cases}
    \begin{alignedat}{2}
    &\sup          &\quad& f^T x  \\
    &\,\text{s.t.} &\quad& Dx \leq c.
    \end{alignedat}
    \end{cases}
  } 
  \arrow[d,"\text{some text here}"]
\\
  C \& D \arrow[l,"\text{some text here}"]
\end{tikzcd}
\end{equation*}
The references are \eqref{eq:1} and \eqref{eq:2}. Another equation to see
that the number is right
\begin{equation}
0=0
\end{equation}

\end{document}

Answer 2

Here is a proposal. The equation numbers on the left and right go back to David Carlisle's answer. So just squeeze these equations in minipages. And instead of having a \quad and \hspace gathering, just use pos=... in order to move the texts around, which are much more straightforward to typeset with \text BTW.

\documentclass{article}
\usepackage{amsmath}
\usepackage{tikz-cd}
\usepackage{hyperref}

% https://tex.stackexchange.com/a/212099/121799
\makeatletter
\newcommand{\leqnomode}{\tagsleft@true\let\veqno\@@leqno}%
\newcommand{\reqnomode}{\tagsleft@false\let\veqno\@@eqno}%
\newcommand*{\compress}{\@minipagetrue}
\makeatother

\begin{document}


\begin{figure}[h]
\begin{equation*}
\begin{tikzcd}[row sep=huge, column sep=width("bbbbbbbbbbbbbbbbbbbbbbb"),
ampersand replacement=\&]  
\begin{minipage}{4cm}
\leqnomode
\begin{equation} \label{eq:1} 
\left\{\begin{array}{rl}
\sup & c^T x  \\
s.t.   & Ax \leq b.
\end{array} \right. 
\end{equation} 
\end{minipage}
   \arrow[r,  "\text{some text here}" pos=0.5]  
        \arrow[d,   "\text{some down text here}"  swap]  \&     
        \arrow[d,  "\text{some down text here}" ] 
\begin{minipage}{4cm}
\begin{equation} \label{eq:2} 
\left\{\begin{array}{rl}
\sup & f^T x  \\
s.t.   & Dx \leq e.
\end{array} \right. 
\end{equation} 
\end{minipage}\\
        C        \& D    
        \arrow[l, "\text{some text here}" pos=0.4 ] \\[-1cm]
\end{tikzcd} 
\end{equation*}
\caption{Figure caption here.}  
\label{figure-commutative} 
\end{figure}

Then I would like to reference \eqref{eq:1} and \eqref{eq:2} here. 

\end{document}