Using \tag in \aligned embedded within \equation environment

Question

I want to tag my equations with parallel aligned environments. The code is shown below

\begin{equation*}
\begin{aligned}
& \bold{H}_1^\top\bold{x}_1^*+\bold{K}_1^\top\bold{y}+\bold{U}(\omega_t)= \bold{r}_1:\\
& \bold{A}_3^\top\bold{y}\leq \bold{b}_3:
\end{aligned}
\qquad
\begin{aligned}
& \boldsymbol{\gamma}_1(\omega_t), \\
& \boldsymbol{\zeta}_1(\omega_t), 
\end{aligned}
\end{equation*}

The output should be two aligned equations, and my goal is to tag them using \tag.

I have tried to add \tag to the first \begin{aligned} block and the second block, but they all failed with an error saying

Package amsmath Error: \tag not allowed here

I have searched the forum but there is none regarding to the tag for double aligned equation. I need to use \begin{equation*} instead of \begin{equation} to allow \tag, since I want to make my own tags.

Thank you in advance!

Gabriel

Answer 1

Maybe it is something like this you're after?

\documentclass[10pt, a5paper]{book}
\usepackage{mathtools, amssymb}
\usepackage[showframe]{geometry} 
\usepackage{tabularx}

\makeatletter
\newcommand*{\compress}{\@minipagetrue}
\thispagestyle{empty}

\begin{document}

\noindent\begin{tabularx}{\linewidth}{@{}>{\hsize=1.2\hsize \compress\arraybackslash}X @{\qquad} >{\hsize=0.8\hsize\compress\arraybackslash}X@{}}
{ \begin{subequations}\begin{align}
& \mathbf{H}_1^\top\mathbf{x}_1^*+\mathbf{K}_1^\top\mathbf{y}+\mathbf{U}(\omega_t)= \mathbf{r}_1:\\
& \mathbf{A}_3^\top\mathbf{y}\leq \mathbf{b}_3:
\end{align}
\end{subequations}}
 &
{ \begin{subequations}\begin{align}
& \boldsymbol{\gamma}_1(\omega_t), \\
& \boldsymbol{\zeta}_1(\omega_t),
\end{align}
\end{subequations}}
\end{tabularx}

\end{document}