A Derivation of Lovász' Theta via Augmented Lagrange Duality

Issue		RAIRO Oper. Res. Volume 37, Number 1, January-March 2003


Page(s)		17 - 27
DOI		10.1051/ro:2003012

RAIRO Oper. Res. 37 (2003) 17-27
DOI: 10.1051/ro:2003012

A Derivation of Lovász' Theta via Augmented Lagrange Duality

Mustapha Ç. Pinar

Bilkent University, Department of Industrial Engineering, 06800 Ankara, Turkey; mustafap@bilkent.edu.tr..
(Received July, 2002.)

Abstract
A recently introduced dualization technique for binary linear programs with equality constraints, essentially due to Poljak et al. [13], and further developed in Lemaréchal and Oustry [9], leads to simple alternative derivations of well-known, important relaxations to two well-known problems of discrete optimization: the maximum stable set problem and the maximum vertex cover problem. The resulting relaxation is easily transformed to the well-known Lovász $\theta$ number.

Mathematics Subject Classification. 90C27, 90C27, 90C35.

Key words: Lagrange duality, stable set, Lovász theta function, semidefinite relaxation.

© EDP Sciences 2003

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