优化问题中的自动编号约束

Question

下面的代码

\documentclass{report}
\begin{document}

\begin{equation}
\setlength\arraycolsep{1.5pt}
\begin{array}{l@{\qquad} r c r c r}
(P)     & z(P) = \min   &  cx \\
        & \mathrm{s.t.} &  Ax & = & b \\
        &               &   x & \in &  X \\
\end{array}
\end{equation}

\end{document}

产生与整个模型相关的单个方程编号，如下图所示。

我如何为每个约束定义一个数字（无需自己编写）？请参阅下面的示例。

Answer 1

此答案使用optidef包。我似乎需要以不同于作为示例发布的内容的方式编写目标函数。否则，函数和约束将单独编号。

以下示例说明了四种不同的用法，提供了不同的对齐方式以及长短表示法。

结果如下：

这是代码：

\documentclass[a4paper,12pt]{report}

\usepackage[nocomma]{optidef}

\begin{document}

Short notation, alternative 1 layout for constraints
\begin{mini!}|s|[1]                   % mini! = minimize 
    {x}                               % optimization variable
    {z(P) = \min cx \label{eq:eq1}}   % objective function and label
    {\label{eq:Example1}}             % label for optimizatio problem
    {}                                % optimization result
    \addConstraint{Ax}{=b \label{eq:con1}}    % constraint 1
    \addConstraint{x}{\in X \label{eq:con2}}  % constraint 2
\end{mini!}

Short notation, alternative 2 layout for constraints
\begin{mini!}|s|[2]                   % mini! = minimize 
    {x}                               % optimization variable
    {z(P) = \min cx \label{eq:eq1}}   % objective function and label
    {\label{eq:Example1}}             % label for optimizatio problem
    {}                                % optimization result
    \addConstraint{Ax}{=b \label{eq:con1}}    % constraint 1
    \addConstraint{x}{\in X \label{eq:con2}}  % constraint 2
\end{mini!}

Short notation, alternative 3 layout for constraints
\begin{mini!}|s|[3]                   % mini! = minimize
    {x}                               % optimization variable
    {z(P) = \min cx \label{eq:eq1}}   % objective function and label
    {\label{eq:Example1}}             % label for optimizatio problem
    {}                                % optimization result
    \addConstraint{Ax}{=b \label{eq:con1}}    % constraint 1
    \addConstraint{x}{\in X \label{eq:con2}}  % constraint 2
\end{mini!}

Long notation, alternative 2 layout for constraints
\begin{mini!}|l|[2]                   % mini! = minimize 
    {x}                               % optimization variable
    {z(P) = \min cx \label{eq:eq1}}   % objective function and label
    {\label{eq:Example1}}             % label for optimizatio problem
    {}                                % optimization result
    \addConstraint{Ax}{=b \label{eq:con1}}    % constraint 1
    \addConstraint{x}{\in X \label{eq:con2}}  % constraint 2
\end{mini!}

\end{document}