eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2016-08-23
78:1
78:14
10.4230/LIPIcs.ICALP.2016.78
article
Tight Sum-Of-Squares Lower Bounds for Binary Polynomial Optimization Problems
Kurpisz, Adam
Leppänen, Samuli
Mastrolilli, Monaldo
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 that 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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol055-icalp2016/LIPIcs.ICALP.2016.78/LIPIcs.ICALP.2016.78.pdf
SoS/Lasserre hierarchy
lift and project methods
binary polynomial optimization