Is there any method to use an automatic word wrap in equations?

Question

In common words, the word wrap is done automatically. But in the equations, it doesn't work. Actually, I am making some presentation material using beamer in Latex.

Is there any way to make word wrap automatically? I hope the first line is left align, simultaneously, second line is right align

My code is like the following:

\begin{frame}[shrink=0, t]{The \textbf{\textit{DP}} Algorithm}
    \begin{center}
        \begin{minipage}{.9\textwidth}
            \begin{proof}

            \begin{enumerate}
            \setcounter{enumi}{4}
            \item Since $\pi^k=\left(\mu_k, \pi^{k+1}\right)$,
            \begin{align*}
                J_k^*(x_k) &= \min_{\left(\mu_k, \pi^{k+1}\right)} \underset{w_k, \cdots, w_{N-1}}{E}
                \left\{ g_k(x_k, \mu_k(x_k), w_k) + g_N(x_N) + \sum_{i=k+1}^{N-1} g_i(x_i, \mu_i(x_i), w_i)\right\}\\
                &= 123
            \end{align*}
            \end{enumerate}
            \end{proof}
        \end{minipage}
    \end{center}
\end{frame}

Answer 1

This is simply to show how to reformat the equation with as little effort as possible. Copy the line to be broken. Use \right. or \left. to balance an otherwise unmatched \left or \right. Use \hphantom to preserve spacing, and \vphantom to preserve the \left ... \right size.

Note, the additional \qquad is to compensate for the missing = and \{.

\documentclass{beamer}
\begin{document}
\begin{frame}[shrink=0, t]{The \textbf{\textit{DP}} Algorithm}
    \begin{center}
        \begin{minipage}{.9\textwidth}
            \begin{proof}

            \begin{enumerate}
            \setcounter{enumi}{4}
            \item Since $\pi^k=\left(\mu_k, \pi^{k+1}\right)$,
            \begin{align*}
                J_k^*(x_k) &= \min_{\left(\mu_k, \pi^{k+1}\right)} \underset{w_k, \cdots, w_{N-1}}{E}
                \left\{ g_k(x_k, \mu_k(x_k), w_k) + g_N(x_N) \vphantom{+ \sum_{i=k+1}^{N-1} g_i(x_i, \mu_i(x_i), w_i)}\right.\\
                &\qquad \hphantom{\min_{\left(\mu_k, \pi^{k+1}\right)} \underset{w_k, \cdots, w_{N-1}}{E}}
                \left. \vphantom{g_k(x_k, \mu_k(x_k), w_k) + g_N(x_N)} + \sum_{i=k+1}^{N-1} g_i(x_i, \mu_i(x_i), w_i)\right\}\\
                &= 123
            \end{align*}
            \end{enumerate}
            \end{proof}
        \end{minipage}
    \end{center}
\end{frame}
\end{document}

Answer 2

You can use breqn package for this:

\documentclass{article}
\usepackage{amsthm,amsmath,breqn,lipsum}
\usepackage[showframe,margin=5cm]{geometry}
\begin{document}
\lipsum[1-2]
\begin{frame}[shrink=0, t]{The \textbf{\textit{DP}} Algorithm}
    \begin{center}
        \begin{minipage}{.9\textwidth}
            \begin{proof}

            \begin{enumerate}
            \setcounter{enumi}{4}
            \item Since $\pi^k=\left(\mu_k, \pi^{k+1}\right)$,
            \begin{dmath*}
                J_k^*(x_k) = \min_{\left(\mu_k, \pi^{k+1}\right)} \underset{w_k, \cdots, w_{N-1}}{E}
                \left\{ g_k(x_k, \mu_k(x_k), w_k) + g_N(x_N) + \sum_{i=k+1}^{N-1} g_i(x_i, \mu_i(x_i), w_i)\right\}\\
                = 123
            \end{dmath*}
            \end{enumerate}
            \end{proof}
        \end{minipage}
    \end{center}
\end{frame}
\lipsum[1-2]
\end{document}