A Comparison of the Sherali-Adams, Lovász-Schrijver, and Lasserre Relaxations for 0–1 Programming
- 1 August 2003
- journal article
- Published by Institute for Operations Research and the Management Sciences (INFORMS) in Mathematics of Operations Research
- Vol. 28 (3), 470-496
- https://doi.org/10.1287/moor.28.3.470.16391
Abstract
Sherali and Adams (1990), Lovász and Schrijver (1991) and, recently, Lasserre (2001b) have constructed hierarchies of successive linear or semidefinite relaxations of a 0–1 polytope P ⫅ ℝn 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.Keywords
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