Small Extended Formulations for Cyclic Polytopes
Optimization and Control
2018-04-18 v2
Abstract
We provide an extended formulation of size O(log n)^{\lfloor d/2 \rfloor} for the cyclic polytope with dimension d and n vertices (i,i^2,\ldots,i^d), i in [n]. First, we find an extended formulation of size log(n) for d= 2. Then, we use this as base case to construct small-rank nonnegative factorizations of the slack matrices of higher-dimensional cyclic polytopes, by iterated tensor products. Through Yannakakis's factorization theorem, these factorizations yield small-size extended formulations for cyclic polytopes of dimension d>2.
Cite
@article{arxiv.1401.8138,
title = {Small Extended Formulations for Cyclic Polytopes},
author = {Yuri Bogomolov and Samuel Fiorini and Aleksandr Maksimenko and Kanstantsin Pashkovich},
journal= {arXiv preprint arXiv:1401.8138},
year = {2018}
}