  Model order reduction (MOR) methods that are designed to preserve structural
features of a given full order model (FOM) often suffer from a lower accuracy
when compared to their non-structure-preserving counterparts. In this paper, we
present a framework for structure-preserving MOR, which allows to compute
structured reduced order models (ROMs) with a much higher accuracy. The
framework is based on parameter optimization, i.e., the elements of the system
matrices of the ROM are iteratively varied to minimize an objective functional
that measures the difference between the FOM and the ROM. The structural
constraints can be encoded in the parametrization of the ROM. The method only
depends on frequency response data and can thus be applied to a wide range of
dynamical systems.
  We illustrate the effectiveness of our method on a port-Hamiltonian and on a
symmetric second-order system in a comparison with other structure-preserving
MOR algorithms.
