Ohlberger, Mario; Schaefer, Michael; Schindler, Felix Localized model reduction in PDE constrained optimization. (English) Zbl 1407.49030 Schulz, Volker (ed.) et al., Shape optimization, homogenization and optimal control. DFG-AIMS workshop held at the AIMS Center Sénégal, Mbour, Sénégal, March 13–16, 2017. Cham: Birkhäuser. ISNM, Int. Ser. Numer. Math. 169, 143-163 (2018). Summary: We present efficient localized model reduction approaches for PDE constraint optimization or optimal control. The first approach focuses on problems where the underlying PDE is given as a locally periodic elliptic multiscale problem. The second approach is more universal and focuses on general underlying multiscale or large scale problems. Both methods make use of reduced basis techniques and rely on an efficient a-posteriori error estimation for the approximation of the underlying parameterized PDE. The methods are presented and numerical experiments are discussed.For the entire collection see [Zbl 1401.49003]. Cited in 4 Documents MSC: 49K20 Optimality conditions for problems involving partial differential equations 65K10 Numerical optimization and variational techniques 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 49N20 Periodic optimal control problems 93A15 Large-scale systems Keywords:localized model reduction; reduced basis methods; optimal control; PDE constrained optimization; LRBMS; heterogeneous multiscale method PDFBibTeX XMLCite \textit{M. Ohlberger} et al., ISNM, Int. Ser. Numer. Math. 169, 143--163 (2018; Zbl 1407.49030) Full Text: DOI