Convex Relaxations and Integrality Gaps

Eden Chlamtac () and Madhur Tulsiani ()
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Eden Chlamtac: Tel Aviv University
Madhur Tulsiani: Toyota Technological Institute at Chicago

Chapter Chapter 6 in Handbook on Semidefinite, Conic and Polynomial Optimization, 2012, pp 139-169 from Springer

Abstract: Abstract We discuss the effectiveness of linear and semidefinite relaxations in approximating the optimum for combinatorial optimization problems. Various hierarchies of these relaxations, such as the ones defined by Lovasz and Schrijver, Sherali and Adams, and Lasserre generate increasingly strong linear and semidefinite programming relaxations starting from a basic one. We survey some positive applications of these hierarchies, where their use yields improved approximation algorithms. We also discuss known lower bounds on the integrality gaps of relaxations arising from these hierarchies, demonstrating limits on the applicability of such hierarchies for certain optimization problems.

Keywords: Chromatic Number; Constraint Satisfaction Problem; Vertex Cover; Semidefinite Program; Linear Program Relaxation (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/978-1-4614-0769-0_6

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