  The goal of this paper is to survey the properties of the eigenvalue
relaxation for least squares binary problems. This relaxation is a convex
program which is obtained as the Lagrangian dual of the original problem with
an implicit compact constraint and as such, is a convex problem with polynomial
time complexity. Moreover, as a main pratical advantage of this relaxation over
the standard Semi-Definite Programming approach, several efficient bundle
methods are available for this problem allowing to address problems of very
large dimension. The necessary tools from convex analysis are recalled and
shown at work for handling the problem of exactness of this relaxation. Two
applications are described. The first one is the problem of binary image
reconstruction and the second is the problem of multiuser detection in CDMA
systems.
