An augmented Lagrangian dual optimization approach to the HH-weighted model updating problem

Model updating for the quadratic eigenvalue problem aims to update the model Q(λ):=λ2M+λC+KQ(λ):=λ2M+λC+K by given eigendata. In this paper, we consider the HH-weighted model updating problem which can not only preserve the symmetry and definiteness of the original model but also express our confidence in the original model through assigning different confidence weights. We propose an augmented Lagrangian dual method for the HH-weighted model updating problem. Under some mild assumptions, our method is shown to converge at least linearly. Numerical results illustrate the effectiveness of our method. In addition, we compare our method with the semi-definite programming (SDP) method. Numerical results illustrate that when the scale of the model becomes large our method still works but the SDP method failed to converge.