A derivation of Lovász' theta via augmented Lagrange duality

A recently introduced dualization technique for binary linear programs with equality constraints, essentially due to Poljak et al. and further developed in Lemaréchal and Oustry, 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 θ-number.