Non-Conforming Localized Model Reduction with Online Enrichment: Towards Optimal Complexity in PDE constrained Optimization

We propose a new non-conforming localized model reduction paradigm for efficient solution of large scale or multiscale PDE constrained optimization problems. The new conceptual approach goes beyond the classical offline/online splitting of traditional projection based model order reduction approaches for the underlying state equation, such as the reduced basis method. Instead of first constructing a surrogate model that has globally good approximation quality with respect to the whole parameter range, we propose an iterative enrichment procedure that refines and locally adapts the surrogate model specifically for the parameters that are depicted during the outer optimization loop.