We study the modeling of non-convex piecewise linear functions as Mixed Integer Programming (MIP) problems. We review several new and existing MIP formulations for continuous piecewise linear functions with special attention paid to multivariate non-separable functions. We compare these formulations with respect to their theoretical properties and their relative computational performance. In addition, we study the extension of these formulations to lower semicontinuous piecewise linear functions.
To appear in Operations Research