1

Please help me to get following set of equation such that I want to number only A_1(\alpha,\beta) \geq r_1;~B_1(\alpha,\beta) \geq r_1 and A_2(\alpha,\beta) \geq r_2; ~ B_2(\alpha,\beta) \geq r_2 as (#a) and (#b).

\begin{prob} \label{p_df_minmax_II}
\begin{equation} \label{e_df_minmax_II}
\begin{aligned}
& \max\limits_{\alpha,\beta}
& & r \\
& \text{s.~t.} 
& &  r_1 \geq r;~r_2 \geq r;~ A_3(\alpha,\beta)  \geq r;\\
& & &  A_1(\alpha,\beta)  \geq r_1;~B_1(\alpha,\beta)  \geq r_1; \\
& & &  A_2(\alpha,\beta)  \geq r_2; ~ B_2(\alpha,\beta)  \geq r_2; \\
& & & \alpha\in[0,1); ~\beta\in[0,1).
\end{aligned}
\end{equation}
\end{prob}

Please note that I need same alignment environment. I know that subequations and eqnarray may help but I could not get the same alignment then.

2

You need subequations for the sub-numbering, but that environment doesn't really have anything to do with the alignment. alignat is an option here I think. Use \nonumber to indicate that a line should not be numbered.

enter image description here

\documentclass[a4paper]{article}
\usepackage{amsmath}

\begin{document}
\begin{subequations} \label{e_df_minmax_II}
\begin{alignat}{2}
& \max\limits_{\alpha,\beta}
&\quad & r \nonumber\\ %note \quad added here
& \text{s.~t.} 
& &  r_1 \geq r;~r_2 \geq r;~ A_3(\alpha,\beta)  \geq r; \nonumber\\
& & &  A_1(\alpha,\beta)  \geq r_1;~B_1(\alpha,\beta)  \geq r_1; \label{eq:AB1} \\
& & &  A_2(\alpha,\beta)  \geq r_2; ~ B_2(\alpha,\beta)  \geq r_2; \label{eq:AB2} \\
& & & \alpha\in[0,1); ~\beta\in[0,1). \nonumber
\end{alignat}
\end{subequations}

\ref{e_df_minmax_II}; \ref{eq:AB1}, \ref{eq:AB2}
\end{document}
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