  In this work we consider the problem of semi-active damping optimization of
mechanical systems with fixed damper positions. Our goal is to compute a
damping that is locally optimal with respect to the $\mathcal{H}_\infty$-norm
of the transfer function from the exogenous inputs to the performance outputs.
We make use of a new greedy method for computing the $\mathcal{H}_\infty$-norm
of a transfer function based on rational interpolation. In this paper, this
approach is adapted to parameter-dependent transfer functions. The
interpolation leads to parametric reduced-order models that can be optimized
more efficiently. At the optimizers we then take new interpolation points to
refine the reduced-order model and to obtain updated optimizers. In our
numerical examples we show that this approach normally converges fast and thus
can highly accelerate the optimization procedure. Another contribution of this
work are heuristics for choosing initial interpolation points.
