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arXiv · 1811.10409

A geometric way to build strong mixed-integer programming formulations

Joey Huchette·Juan Pablo Vielma
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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.

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Joey Huchette, Juan Pablo Vielma. 2018-11-22. A geometric way to build strong mixed-integer programming formulations. https://arxiv.org/abs/1811.10409

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