English

A geometric way to build strong mixed-integer programming formulations

Optimization and Control 2019-10-11 v4

Abstract

We give an explicit geometric way to build mixed-integer programming (MIP) formulations for unions of polyhedra. The construction is simply described in terms of spanning hyperplanes in an r-dimensional linear space. The resulting MIP formulation is ideal, and uses exactly r integer variables and 2 x (# of spanning hyperplanes) general inequality constraints. We use this result to derive novel logarithmic-sized ideal MIP formulations for discontinuous piecewise linear functions and structures appearing in robotics and power systems problems.

Keywords

Cite

@article{arxiv.1811.10409,
  title  = {A geometric way to build strong mixed-integer programming formulations},
  author = {Joey Huchette and Juan Pablo Vielma},
  journal= {arXiv preprint arXiv:1811.10409},
  year   = {2019}
}

Comments

arXiv admin note: text overlap with arXiv:1709.10132

R2 v1 2026-06-23T05:28:06.731Z