Nonconvex Piecewise Linear Functions: Advanced Formulations and Simple Modeling Tools

Piecewise linear functions are deceptively simple structures that nonetheless capable of approximating complex nonlinear behavior. As such, they have been adopted throughout operations research and engineering to approximate in optimization problems which would otherwise render the problem extremely difficult solve. In “Nonconvex Linear Functions: Advanced Formulations Simple Modeling Tools,” J. Huchette P. Vielma derive new mixed-integer programming (MIP) formulations for embedding low-dimensional nonconvex piecewise models. These computationally outperform crowded field existing approaches a number regimes interest. these derived using recently developed machinery produce highly performant, but uninterpretable, formulations, authors showcase utility high-level modeling tools by presenting PiecewiseLinearOpt.jl, an extension popular JuMP language implements host MIP function single, easy-to-use interface.