$f(a) = \begin{cases} a & a \ge 1 \\ 2a-1 & a\lt 1 \end{cases}$
$\text{minimize } f(u_1) + f(u_2)$
$\begin{align*} \text{s.t. } &\text{some constraints involving } u_1, u_2\\ & \text{some constraints involving } f(u_1), f(u_2) \end{align*}$
I know that you can formulate non-smooth functions such as max, min, absolute value as LP. Is it possible to express if statement as LP?
If so, you can provide an example on how to do so
Note: If you can provide a link to a textbook that describe this in depth, it would be appreciated too