On the minimization of quadratic functions with bilinear constraints via augmented Lagrangians

The minimization of a quadratic function subject to bilinear constraints is proven to be equivalent to the unconstrained minimization of an augmented Lagrangian of the type introduced by Di Pillo and Grippo, under assumptions weaker than those used in the general case. Two applications are reported: the parameter identification problem for a discrete linear system and the optimal control of a bilinear discrete system.