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}
\label{eq:1}
they work but will be confusing for anyone looking at the source if the printed numbers are different.[H]
takes the figure out of the current context (so for example it is not set as part of a list) The only reason to usefigure
is to specify that it may move, if you don't want it to move just don't usefigure
equations are almost never put in floating environments such as figure.