Linear programming, a non standard handling of absolute value
Your formulation ensures that $|x_i|=t_i$ in every optimal solution. However, this does not hold for an arbitrary feasible point. 

Picky people could then complain that your formulation isn't entirely correct. However, as long as you don't change your objective function nor use $t_i$ in any other constraint, then you will be fine in practice.

This blog post describes several ways to model absolute values.