在案例环境中对齐多行方程

Question

我有一个等式：

由以下代码片段生成：

Secondly, instead of simultaneously minimizing the mean and standard deviation of the objective(s),
another type of formulation of robust optimization considers the standard deviation as the constraint:

\begin{flalign}\label{eq:robust-optimization-2}
    \text{Type II:}
    \begin{cases}
        \text{find}       &\vect{x} \\
        \text{minimizing} &\mu\left\{f_{i}(\vect{x}, \vect{p})\right\} (i = 1, ...\, , n_{\text{objectives}}) \\
        \text{subject to} &\sigma\left\{f_{i}(\vect{x}, \vect{p})\right\} \leq \sigma_{i}^{\text{crit}} (i = 1, ...\, , n_{\text{objectives}}) \\
                          &L_{j}(\vect{x}, \vect{p}) \leq 0 (j = 1, ...\, , n_{\text{constraints}}) \\
                          &\vect{x}^{-} \leq \vect{x} \leq \vect{x}^{+}
    \end{cases}
\end{flalign}

Thirdly, as previously discussed, in the robust design optimization problem as formulated by

我该如何修改我的代码以满足以下两个要求（棕色和绿色）同时其他内容保持不变？

Answer 1

只需使用equation环境并嵌套aligned案例：

\documentclass{article}
\usepackage{empheq}
\let\vect = \mathbf

\begin{document}

Secondly, instead of simultaneously minimizing the mean and standard deviation of the objective(s),
another type of formulation of robust optimization considers the standard deviation as the constraint:

\begin{equation}\label{eq:robust-optimization-2}
    \text{Type II:}
    \begin{cases}\begin{aligned}
         & \text{find} & &\vect{x} \\
         & \text{minimizing} & &\mu\left\{f_{i}(\vect{x}, \vect{p})\right\} & & (i = 1, ...\, , n_{\text{objectives}}) \\
         & \text{subject to} & & \sigma\left\{f_{i}(\vect{x}, \vect{p})\right\} \leq \sigma_{i}^{\text{crit}} & & (i = 1, ...\, , n_{\text{objectives}}) \\
                    & & &L_{j}(\vect{x}, \vect{p}) \leq 0 & & (j = 1, ...\, , n_{\text{constraints}}) \\
                    & & &\vect{x}^{-} \leq \vect{x} \leq \vect{x}^{+}
    \end{aligned}\end{cases}
\end{equation}

Thirdly, as previously discussed, in the robust design optimization problem as formulated by

\end{document} 

Answer 2

在包中定义fleqn环境nccmath：

\documentclass{article}
\usepackage{bm}
\usepackage{nccmath}

\begin{document}
\begin{fleqn}
\begin{align}\label{eq:robust-optimization-2}
\text{Type II:}
    \left\{\begin{aligned}
        \text{find}       &&& \bm{x} \\
        \text{minimizing} &&& \mu\left\{f_{i}(\bm{x}, \bm{p})\right\}
                            &&   (i = 1, ...\, , n_{\text{objectives}}) \\
        \text{subject to} &&& \sigma\left\{f_{i}(\bm{x}, \bm{p})\right\} \leq \sigma_{i}^{\text{crit}}
                            &&   (i = 1, ...\, , n_{\text{objectives}}) \\
                          &&& L_{j}(\bm{x}, \bm{p}) \leq 0
                            &&   (j = 1, ...\, , n_{\text{constraints}}) \\
                          &&&\bm{x}^{-} \leq \bm{x} \leq \bm{x}^{+}
                            &&
        \end{aligned}\right.
\end{align}
\end{fleqn}
\end{document}

（红线表示文本区域边框）