Fit equation with \cases in page width using \resizebox

Question

I'm trying to fit an equation with several cases into my page width. The pain is that one case is awfully long. I used the \resizebox{} approach (see solution here), which would work, if there would be no \begin{cases}.

I learned that \resizebox creates a 'new' box and within this box there is no math environment, which is the reason why the solution math content starts with an $, to trigger the inline math mode. My problem is that \begin{cases} is not suitable for the inline math mode, and I receive a 'Missing $ inserted.' error.

Do you have an alternative approach to solve this issue. Adding another \begin{equation} within the box does not work. The work compiles but I would love to see a smoother solution than latex putting $ by itself. - Thanks!

Code looks like this:

\begin{equation}
\resizebox{.9\hsize}{!}{
  r(b_{i,t}^C,p_{market,t})= \begin{cases}  
    -(b_{i,t}^C - p_{market,t})^2,      & \text{if} b_{i,t}^C > p_{market,t}\\
    -(b_{i,t}^C - p_{grid})^2,          & \text{if} b_{i,t}^C < p_{market,t} \\
    \frac{p_{market,t}}{100} + \theta,  & \text{if} b_{i,t}^C = p_{market,t} \\
    \frac{p_{market,t}}{100} + 2\theta, & \text{if} b_{i,t}^C = p_{market,t} \text{and} b_{i,t}^C < min(b_{i,t-j}^C,.., b_{i,t-1}^C) \quad|  b_{i,t-j}^C=p_{market,t-j} 
 \end{cases}
 }
\end{equation}

Answer 1

You can split the long condition into three lines.

\documentclass{article}
\usepackage{amsmath}

\begin{document}

\begin{equation}
  r(b_{i,t}^C,p_{\mathrm{market},t})=
  \begin{cases}  
    -(b_{i,t}^C - p_{\mathrm{market},t})^2,
      & \text{if } b_{i,t}^C > p_{\mathrm{market},t} \\[2ex]
    -(b_{i,t}^C - p_{\mathrm{grid}})^2,
      & \text{if } b_{i,t}^C < p_{\mathrm{market},t} \\[2ex]
    \frac{p_{\mathrm{market},t}}{100} + \theta,
      & \text{if } b_{i,t}^C = p_{\mathrm{market},t} \\[2ex]
    \frac{p_{\mathrm{market},t}}{100} + 2\theta,
      & \begin{aligned}[t]
        &\text{if } b_{i,t}^C = p_{\mathrm{market},t} \text{ and} \\
        &b_{i,t}^C < \min(b_{i,t-j}^C,\dots, b_{i,t-1}^C) \\
        &\mid b_{i,t-j}^C=p_{\mathrm{market},t-j}
        \end{aligned}
  \end{cases}
\end{equation}

\end{document}

Note \mathrm{market}, \mathrm{grid}, \dots and \min.

Answer 2

The following solution shortens some of the expressions by putting p^*=p_{market}. This, in turns, allows displaying the conditions for the final case in just two rows.

\documentclass{article}
\usepackage{mathtools}         % for 'dcases' env.
\newcommand\vn[1]{\mathrm{#1}} % use mathrm display variable names
\begin{document}

\noindent
Put $p^*_t=p_{\vn{market},t}$. Then
\begin{equation}
r(b_{i,t}^C,p^*_t)= 
\begin{dcases}  
  -(b_{i,t}^C - p^*_t)^2         & \text{if $b_{i,t}^C > p^*_t$} \\
  -(b_{i,t}^C - p_{\vn{grid}})^2 & \text{if $b_{i,t}^C < p^*_t$} \\
  p^*_t/100 + \theta             & \text{if $b_{i,t}^C = p^*_t$} \\
  p^*_t/100 + 2\theta            & \text{if $b_{i,t}^C = p^*_t$ and} \\
       & b_{i,t}^C < \min(b_{i,t-j}^C,\dots, b_{i,t-1}^C) 
       \mid b_{i,t-j}^C=p^*_{t-j}
\end{dcases}
\end{equation}

\end{document}