  This thesis presents recent advances in model order reduction methods with
the primary aim to construct online-efficient reduced surrogate models for
parameterized multiscale phenomena and accelerate large-scale PDE-constrained
parameter optimization methods. In particular, we present several different
adaptive RB approaches that can be used in an error-aware trust-region
framework for progressive construction of a surrogate model used during a
certified outer optimization loop. In addition, we elaborate on several
different enhancements for the trust-region reduced basis (TR-RB) algorithm and
generalize it for parameter constraints. Thanks to the a posteriori error
estimation of the reduced model, the resulting algorithm can be considered
certified with respect to the high-fidelity model. Moreover, we use the
first-optimize-then-discretize approach in order to take maximum advantage of
the underlying optimality system of the problem. In the first part of this
thesis, the theory is based on global RB techniques that use an accurate FEM
discretization as the high-fidelity model. In the second part, we focus on
localized model order reduction methods and develop a novel online efficient
reduced model for the localized orthogonal decomposition (LOD) multiscale
method. The reduced model is internally based on a two-scale formulation of the
LOD and, in particular, is independent of the coarse and fine discretization of
the LOD. The last part of this thesis is devoted to combining both results on
TR-RB methods and localized RB approaches for the LOD. To this end, we present
an algorithm that uses adaptive localized reduced basis methods in the
framework of a trust-region localized reduced basis (TR-LRB) algorithm. The
basic ideas from the TR-RB are followed, but FEM evaluations of the involved
systems are entirely avoided.
