Tight Sum-of-Squares lower bounds for binary polynomial optimization problems [article]

Adam Kurpisz, Samuli Leppänen, Monaldo Mastrolilli
2016 arXiv   pre-print
We give two results concerning the power of the Sum-of-Squares(SoS)/Lasserre hierarchy. For binary polynomial optimization problems of degree 2d and an odd number of variables n, we prove that n+2d-1/2 levels of the SoS/Lasserre hierarchy are necessary to provide the exact optimal value. This matches the recent upper bound result by Sakaue, Takeda, Kim and Ito. Additionally, we study a conjecture by Laurent, who considered the linear representation of a set with no integral points. She showed
more » ... at the Sherali-Adams hierarchy requires n levels to detect the empty integer hull, and conjectured that the SoS/Lasserre rank for the same problem is n-1. We disprove this conjecture and derive lower and upper bounds for the rank.
arXiv:1605.03019v1 fatcat:fa4fy753kndgvlk6pals7jjspq