如何在兩列文檔的推論中寫出長不等式

Question

我想寫下這個推論。它包含兩個不等式，如下面的螢幕截圖所示。我在背面使用兩列IEEEtran文檔類別——目前在 TeX Live 2022 中使用。

作為說明，儘管方程式 (1) 和 (2) 看起來並不簡潔，但預期結果與此類似。

\documentclass[journal]{IEEEtran}
\usepackage{mathtools}
\usepackage{amsmath}
\begin{document}

\begin{corollary}\label{Corollary:new_seq}
Supposing that $i^{\ast} = argmax_i R_3(i)$ and $i^{\ast\ast} = argmax_i R_4(i)$ for all   $i=1,\ldots,n$, if $max (R_3(i),R_4(i)) \geq max(R_5(A^{\prime}),R_6(A^{\prime\prime}))$ in a serial configuration, then the new sequence is optimal when one of the following constraints is fulfilled.

\renewcommand{\labelenumi}{(\roman{enumi})}
\begin{enumerate}
    \item 
    \begin{equation} \label{eq:corollary_i}
    max_{i^{\ast} =1,...,n} (q_i^{\ast}\cdot p_i^{\ast} + (1-q_i^{\ast})c_i^{\ast} \quad  \forall i^{\ast}\geq(n-1), q_i^{\ast}\cdot c_i^{\ast} + (1-q_i^{\ast})p_i^{\ast} \quad   \text{for $i^{\ast} = n$}) \geq (n-1)w + nv
    \end{equation}
 
    \item
    \begin{equation} \label{eq:corollary_ii}
    max_{i^{\ast\ast} =1,...,n} (q_i^{\ast\ast}\cdot p_i^{\ast\ast} + (1-q_i^{\ast\ast})c_i^{\ast\ast} \quad  \forall i^{\ast\ast}\geq(n-1), q_i^{\ast\ast}\cdot c_i^{\ast\ast} + (1-q_i^{\ast\ast})p_i^{\ast\ast} \quad  \text{for $i^{\ast} = n$}) \geq (n+1)w + (n+2)v
    \end{equation}    
\end{enumerate}
\end{corollary}
\end{document}

然而，方程式(i)和(ii)都超出如下列。

請問有人可以建議如何處理該程式碼嗎？如果您有其他選擇來使寫作更整潔，請告訴我。先感謝您。

Answer 1

我不會同時使用枚舉標籤和方程式標籤來標記不等式。由於無論如何您都需要枚舉標籤，因此我將放棄方程式標籤。在下面的程式碼中，我設定了枚舉，以便可以輕鬆地交叉引用項目。

\documentclass[journal]{IEEEtran}
\usepackage{mathtools}
%\usepackage{amsmath} % amsmath is loaded automatically by mathtools
\DeclareMathOperator{\argmax}{argmax}
\usepackage{amsthm}
\newtheorem{corollary}{Corollary}
\usepackage{newtxmath}
\usepackage{enumitem}

\begin{document}

\begin{corollary}\label{Corollary:new_seq}
Suppose that $i^{\ast} = \argmax_i R_3(i)$ and 
$i^{\ast\ast} = \argmax_i R_4(i)$ for $i\in\{1,\dots,n\}$. 
If $\max (R_3(i),R_4(i)) \geq \max(R_5(A'),R_6(A''))$ 
in a serial configuration, then the new sequence is 
optimal if one of the following constraints is 
ful\-filled.
\begin{enumerate}[label=\textup{C.\roman*)},
                  ref= C.\roman*,
                  left=0pt, align=left]
\item \label{item:corollary_i}
\parbox[t]{0.8\columnwidth}{\raggedright$ 
    \max\limits_{i^{\ast} =1,\dots,n}
    \bigl\{
    q_i^{\ast} p_i^{\ast} + (1-q_i^{\ast})c_i^{\ast} 
    \textup{ for all $i^{\ast}\leq n-1$},\allowbreak 
    q_i^{\ast} c_i^{\ast} + (1-q_i^{\ast})p_i^{\ast} 
    \textup{ for $i^{\ast} = n$}
    \bigr\} 
    \geq (n-1)w + nv$}

\bigskip
\item \label{item:corollary_ii}
\parbox[t]{0.87\columnwidth}{\raggedright$
    \max\limits_{i^{\ast\ast} =1,\dots,n}
    \bigl\{
    q_i^{\ast\ast} p_i^{\ast\ast} + (1-q_i^{\ast\ast}) c_i^{\ast\ast} 
    \textup{ for all $i^{\ast\ast}\leq n-1$},\allowbreak
     q_i^{\ast\ast} c_i^{\ast\ast} + (1-q_i^{\ast\ast})p_i^{\ast\ast} 
    \textup{ for $i^{\ast} = n$}
    \bigr\} 
    \geq (n+1)w + (n+2)v$}
\end{enumerate}
\end{corollary}

If one of the constraints \ref{item:corollary_i} or 
\ref{item:corollary_ii} is fulfilled, \dots
\end{document}