DROPS

Document

DOI: 10.4230/LIPIcs.ICALP.2016.78

Tight Sum-Of-Squares Lower Bounds for Binary Polynomial Optimization Problems

Authors: Adam Kurpisz, Samuli Leppänen, and Monaldo Mastrolilli

Published in: LIPIcs, Volume 55, 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)

Abstract

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.

Cite as

Adam Kurpisz, Samuli Leppänen, and Monaldo Mastrolilli. Tight Sum-Of-Squares Lower Bounds for Binary Polynomial Optimization Problems. In 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 55, pp. 78:1-78:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

Copy BibTex To Clipboard

@InProceedings{kurpisz_et_al:LIPIcs.ICALP.2016.78,
  author =	{Kurpisz, Adam and Lepp\"{a}nen, Samuli and Mastrolilli, Monaldo},
  title =	{{Tight Sum-Of-Squares Lower Bounds for Binary Polynomial Optimization Problems}},
  booktitle =	{43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)},
  pages =	{78:1--78:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-013-2},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{55},
  editor =	{Chatzigiannakis, Ioannis and Mitzenmacher, Michael and Rabani, Yuval and Sangiorgi, Davide},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2016.78},
  URN =		{urn:nbn:de:0030-drops-63368},
  doi =		{10.4230/LIPIcs.ICALP.2016.78},
  annote =	{Keywords: SoS/Lasserre hierarchy, lift and project methods, binary polynomial optimization}
}

Search Results

Documents authored by Leppänen, Samuli

Tight Sum-Of-Squares Lower Bounds for Binary Polynomial Optimization Problems

Abstract

Cite as

Thanks for your feedback!

Could not send message