  A novel method for performing model updating on finite element models is
presented. The approach is particularly tailored to modal analyses of
buildings, by which the lowest frequencies, obtained by using sensors and
system identification approaches, need to be matched to the numerical ones
predicted by the model. This is done by optimizing some unknown material
parameters (such as mass density and Young's modulus) of the materials and/or
the boundary conditions, which are often known only approximately. In
particular, this is the case when considering historical buildings.
  The straightforward application of a general-purpose optimizer can be
impractical, given the large size of the model involved. In the paper, we show
that, by slightly modifying the projection scheme used to compute the
eigenvalues at the lowest end of the spectrum one can obtain local parametric
reduced order models that, embedded in a trust-region scheme, form the basis
for a reliable and efficient specialized algorithm.
  We describe an optimization strategy based on this approach, and we provide
numerical experiments that confirm its effectiveness and accuracy.
