Year: 2017
Type: preprint
Abstract: We present novel mixed-integer programming (MIP) formulations for optimization over nonconvex piecewise linear functions. We exploit recent advances in the systematic construction of MIP formulations to derive new formulations for univariate functions using a geometric approach, and for bivariate functions using a combinatorial approach. All formulations are strong, small (so-called logarithmic formulations), and have other desirable computational properties. We present extensive experiments in which they exhibit substantial computational performance improvements over existing approaches. To accompany these advanced formulations, we present PiecewiseLinearOpt, an extension of the JuMP modeling language in Julia that implements our models (alongside other formulations from the literature) through a high-level interface, hiding the complexity of the formulations from the end-user.
Source: arXiv (Cornell University)
Authors: Huchette, Joey, Vielma, Juan Pablo
Institutions: Rice University, Massachusetts Institute of Technology
Language: English
Subfield: Numerical Analysis
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4297747509