piecewise linear functions

Spatial branch-and-bound for non-convex separable piecewise-linear optimization

  • Thomas Hübner
  • Akshay Gupte
  • Steffen Rebennack
    • Categories (Mixed) Integer Linear Programming, Global Optimization Tags , ,

    Nonconvex separable piecewise-linear functions (PLFs) are widespread in Operations Research due to their frequent appearance in applications and their use to approximate nonlinearitites. Commonly, nonconvex PLFs are approached from the perspective of discrete optimisation, using special ordered sets and mixed integer linear programs (MILPs). In contrast, we take the viewpoint of global continuous optimization and … Read more

    Mixed-Integer Models for Nonseparable Piecewise Linear Optimization: Unifying Framework and Extensions

  • Shabbir Ahmed
  • George L. Nemhauser
  • Juan Pablo Vielma
    • Categories (Mixed) Integer Linear Programming Tags ,

    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 … Read more