  Piecewise linearization is a key technique for solving nonlinear problems in
transportation network design and other optimization fields, in which
generating breakpoints is a fundamental task. This paper proposes an optimal
breakpoint selection method, rotational adjusting method (RAM), to minimize the
approximation error between the original function and the piecewise linear
function with limited number of pieces, applicable to both convex or concave
function. RAM rotationally adjusts the location of breakpoints based on its
adjacent breakpoints, and the optimal positions would be reached after several
iterations. The optimality of the method is proved. Numerical experiments are
conducted on the logarithmic function.
