Unifying semidefinite and set-copositive relaxations of binary problems and randomization techniques

Felix Lieder (), Fatemeh Rad and Florian Jarre

Computational Optimization and Applications, 2015, vol. 61, issue 3, 669-688

Abstract: A reformulation of quadratically constrained binary programs as duals of set-copositive linear optimization problems is derived using either $$\{0,1\}$$ { 0 , 1 } -formulations or $$\{-1,1\}$$ { - 1 , 1 } -formulations. The latter representation allows an extension of the randomization technique by Goemans and Williamson. An application to the max-clique problem shows that the max-clique problem is equivalent to a linear program over the max-cut polytope with one additional linear constraint. This transformation allows the solution of a semidefinite relaxation of the max-clique problem with about the same computational effort as the semidefinite relaxation of the max-cut problem—independent of the number of edges in the underlying graph. A numerical comparison of this approach to the standard Lovasz number concludes the paper. Copyright Springer Science+Business Media New York 2015

Keywords: Max-cut relaxation; Max-clique problem; Semidefinite program; Completely positive program (search for similar items in EconPapers)
Date: 2015
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://hdl.handle.net/10.1007/s10589-015-9731-y (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:coopap:v:61:y:2015:i:3:p:669-688

Ordering information: This journal article can be ordered from
http://www.springer.com/math/journal/10589

DOI: 10.1007/s10589-015-9731-y

Access Statistics for this article

Computational Optimization and Applications is currently edited by William W. Hager

More articles in Computational Optimization and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().