Certified Nonlinear Parameter Optimization with Reduced Basis Surrogate Models
PDE-constrained parameter optimization problems suffer from the high dimensionality of the corresponding discretizations, which results in long optimization runtimes. One possible approach to solve such large scale optimization problems more rapidly is to replace the PDE constraint by a low-dimensional model constraint obtained via model reduction. We present a general technique for certification of such surrogate optimization results by a-posteriori error estimation based on Reduced Basis (RB) models. We allow arbitrary PDEs and optimization functionals, in particular cover nonlinear optimization problems. Experiments on a stationary heat-conduction problem demonstrate the applicability of the error bound. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)