I am trying to analytically calculate minimum (function is convex, thus minimum) of a piecewise affine function:
$f(x) = max\{ a_1^Tx+b, \dots, a_n^Tx+b \}$
The only possible solution I see here is to plot the function and read it from plot, I am unable to cope doing it analytically. Could somebody give me a hint how could be done?