I want to model a linear optimization problem where the objective is piecewise linear i.e.
$ f(x) = A*x+b $ if $x \leq x^*$
$ f(x) = C*x+d $ if $x > x^*$
How can I model it as a linear objective that could "automatically" affect the right value depending on $x$ value (i.e. : how to "give it" to a solver) ?
Thanks for help !