表格中含有 \argmin 的方程

Question

我希望方程式能够在表格底部正确显示带有变量的 argmin 标签。在​​我的情况下，它显示为下标。我尝试了所有方法，但无法完成。以下是我的代码的一部分，编译正常，但不符合预期

\multicolumn{4}{l}{ $\begin{array} {lcl} \mathbf{r}^i \longleftarrow \argmin_\mathbf{r}\;\Vert \mathbf{r}  \Vert_1 \;\;\;\;\mbox{subject to}\;\;\;\;   \mathbf{y}= \mathbf{A}\mathbf{r} \end{array} $ }
\begin{tabular}{ll|l|l|l|} \hline
\multicolumn{5}{l}{Algorithm:}                                                    \\ \hline
\multicolumn{5}{l}{\begin{tabular}[l]{@{}l@{}}Inputs: CS measurement vector for a speech frame $\mathbf{y}$ \\ Outputs: predictor $\mathbf{a}^i$, residual $\mathbf{r}^i$ \\ $i$ = 0, \\ Initialize dictionary: $h^i=rand, \mathbf{H}^i= conv(h)$             \\\end{tabular}} \\ 
\hline
\multicolumn{5}{l}{\textbf{while} halting criterion false \textbf{do}}        \\ 
\multirow{2}{*}{1.}           &                          \\
                              & \multicolumn{4}{l}{$\begin{array} {lcl} 
                              \mathbf{x}^i =\mathbf{H}^i\mathbf{r}^i \end{array}$}                           \\
2.                            & \multicolumn{4}{l}{
$\begin{array} {lcl} \mathbf{a}^i \longleftarrow \argmin_\mathbf{a} \; \Vert \mathbf{r}\Vert_2 + \gamma\Vert\mathbf{a}\Vert_1 \;\;\; \mbox{subject to}\;\; \mathbf{x}^i=\mathbf{X}^i\mathbf{a+r} \end{array}$\vspace{1em}}                        \\
\multirow{4}{*}{3.}           & \multicolumn{4}{l}{\; \mbox{Estimate the vocal tract impulse response}}                         \\
                              & \multicolumn{4}{l}{
                             $\begin{array} {lcl} 
                              h^{i+1} \;\; \mbox{given the predictior estimate}\;\;\mathbf{a}^i \end{array}$}                           \\
                              & \multicolumn{4}{l}{$\begin{array} {lcl}
                              \mathbf{H}^{i+1}= [conv(h^{i+1})] \end{array}$ 
                                            }            \\
                              & \multicolumn{4}{l}{$\begin{array} {lcl}
                              i=i+1; \end{array}$         }                              \\
\multicolumn{5}{l}{\textbf{end while}} \\ \hline                                        
\end{tabular}

所需输出需要底部带有变量的 argmin，而不是像这样的下标

Answer 1

一个合理的定义方法\argmin是通过\DeclareMathOperator命令amsopn加载，最方便的是通过mathtools。要使限制表现得像那些，\lim您应该使用声明的星号版本：

\DeclareMathOperator*{\argmin}{argmin}

然后，在显示的数学中，限制将放置在文本“argmin”下。如果您在内联数学中，您可以使用\limits或\displaystyle来获得此效果：

\documentclass{article}

\usepackage{mathtools}
\DeclareMathOperator*{\argmin}{argmin}

\begin{document}

\( \argmin_r \) vs.\ \( \argmin\limits_r \),
\begin{equation*}
  \argmin_r
\end{equation*}
and \( \displaystyle\argmin_r \).

\end{document}

对于您的示例代码，您似乎试图显示一种算法。我强烈建议您为此使用algorithm和algorithmic包，而不是多个tabular包。在不知道您的算法到底是什么的情况下，类似以下内容似乎接近所需的输出：

\documentclass{article}

\usepackage{algorithm,algorithmic,mathtools}

\renewcommand{\algorithmicrequire}{\textbf{Input:}}
\renewcommand{\algorithmicensure}{\textbf{Output:}}

\DeclareMathOperator*{\argmin}{argmin}
\DeclareMathOperator{\conv}{conv}

\DeclarePairedDelimiter{\norm}{\lVert}{\rVert}

\begin{document}

\begin{algorithm}
  \caption{Example algorithm}
  \begin{algorithmic}[1]
    \REQUIRE CS measurement vector for a speech frame \( \mathbf{y} \)
    \ENSURE predictor \( \mathbf{a}^i \), residual \( \mathbf{r}^i \)
    \STATE \( i=0 \)
    \STATE Initialize dictionary: \( h^i=\text{rand} \), \(
    \mathbf{H}^i= \conv(h) \)
    \STATE \( \mathbf{r}^i \longleftarrow \argmin\limits_{\mathbf{r}}
    \norm{\mathbf{r}}_1 \) subject to \( \mathbf{y}=
    \mathbf{A}\mathbf{r}   \)
    \WHILE{halting criterion false}
    \STATE \( \mathbf{x}^i =\mathbf{H}^i\mathbf{r}^i \)
    \STATE \( \mathbf{a}^i \longleftarrow \argmin\limits_{\mathbf{a}}
    \norm{\mathbf{r}}_2 + \gamma\norm{\mathbf{a}}_1  \) subject to \(
    \mathbf{x}^i=\mathbf{X}^i\mathbf{a+r} \)
    \STATE Estimate the vocal tract impulse response
    \STATE \( h^{i+1} \) given the predictior estimate \( \mathbf{a}^i \)
    \STATE \( \mathbf{H}^{i+1}= [conv(h^{i+1})] \)
    \STATE \( i=i+1 \)
    \ENDWHILE
  \end{algorithmic}
\end{algorithm}

\end{document}