How to break line of subscript under min?

Question

$$
\min_{c^{(1)}, c^{(2)}, \cdots, c^{(m)}; \\ \mu_1, \mu_2, \cdots, \mu_K}
\frac{1}{m}
\sum_{i=1}^m \left\lVert \vec{x}^{(i)} - \mu_{c^{(i)}} \right\rVert
$$

The \\ does not seem to do the trick? How?

Answer 1

You can use a \substack:

Notes:

• Why is \[ ... \] preferable to $$ ... $$?

Code:

\documentclass{article}
\usepackage{amsmath}
\begin{document}
[
\min_{\substack{c^{(1)}, c^{(2)}, \cdots, c^{(m)}; \ \mu_1, \mu_2, \cdots, \mu_K}}
\frac{1}{m}
\sum_{i=1}^m \left\lVert \vec{x}^{(i)} - \mu_{c^{(i)}} \right\rVert
]
\end{document}

Answer 2

An alternative version, without \substack, but with some additional work:

\documentclass{article}
\usepackage{amsmath}

\begin{document}


\[
\min_{\begin{array}{c}\scriptstyle c^{(1)}, c^{(2)}, \cdots, c^{(m)}; \\[-4pt]
\scriptstyle \mu_1, \mu_2, \cdots, \mu_K
\end{array}
}
\frac{1}{m}
\sum_{i=1}^m \left\lVert \vec{x}^{(i)} - \mu_{c^{(i)}} \right\rVert
\]

\end{document}

I would also recommend replacing \cdots by \ldots or \dots.