Tight rank lower bounds for the Sherali–Adams proof system
Theoretical Computer Science
The integer hull of a convex rational polytope
ICCSA'03 Proceedings of the 2003 international conference on Computational science and its applications: PartIII
| Hi-index | 0.00 |
Sherali and Adams [SA90], Lov\''asz and Schrijver [LS91] and, recently, Lasserre [Las01b] have proposed lift and project methods for constructing hierarchies of successive linear or semidefinite relaxations of a $0-1$ polytope $P\subseteq \oR^n$ converging to $P$ in $n$ steps. Lasserre''s approach uses results about representations of positive polynomials as sums of squares and the dual theory of moments. We present the three methods in a common elementary framework and show that the Lasserre construction provides the tightest relaxations of $P$. As an application this gives a direct simple proof for the convergence of the Lasserre''s hierarchy. We describe applications to the stable set polytope and to the cut polytope.