Mixed-Integer Models for Nonseparable Piecewise-Linear Optimization: Unifying Framework and Extensions - Vielma, Juan Pablo; Ahmed, Shabbir; Nemhauser, George (Operations Research, 2010)
We study the modeling of nonconvex 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 nonseparable 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.