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Kissing Polytopes

Mathematics of Data & Decisions

Speaker: Antoine Deza, McMaster University
Location: 2112 MSB
Start time: Tue, Oct 24 2023, 1:10PM

We investigate the following question: how close can two disjoint lattice polytopes contained in a fixed hypercube be? This question stems from various contexts where the minimal distance between such polytopes appears in complexity bounds of optimization algorithms. We provide nearly matching lower and upper bounds on this distance and discuss its exact computation. We also give similar bounds in the case of disjoint rational polytopes whose binary encoding length is prescribed. This is joint work with Shmuel Onn, Sebastian Pokutta, and Lionel Pournin.