Sum-of-squares hierarchy lower bounds for symmetric formulations
Abstract
We introduce a method for proving Sum-of-Squares (SoS)/ Lasserre hierarchy lower bounds when the initial problem formulation exhibits a high degree of symmetry. Our main technical theorem allows us to reduce the study of the positive semidefiniteness to the analysis of "well-behaved" univariate polynomial inequalities. We illustrate the technique on two problems, one unconstrained and the other with constraints. More precisely, we give a short elementary proof of Grigoriev/Laurent lower bound for finding the integer cut polytope of the complete graph. We also show that the SoS hierarchy requires a non-constant number of rounds to improve the initial integrality gap of 2 for the Min-Knapsack linear program strengthened with cover inequalities.
Keywords
Cite
@article{arxiv.1407.1746,
title = {Sum-of-squares hierarchy lower bounds for symmetric formulations},
author = {Adam Kurpisz and Samuli Leppänen and Monaldo Mastrolilli},
journal= {arXiv preprint arXiv:1407.1746},
year = {2016}
}