Author:
Keil Tim,Mechelli Luca,Ohlberger Mario,Schindler Felix,Volkwein Stefan
Abstract
In this contribution we propose and rigorously analyze new variants of adaptive Trust-Region methods for parameter optimization with PDE constraints and bilateral parameter constraints. The approach employs successively enriched Reduced Basis surrogate models that are constructed during the outer optimization loop and used as model function for the Trust-Region method. Each Trust-Region sub-problem is solved with the projected BFGS method. Moreover, we propose a non-conforming dual (NCD) approach to improve the standard RB approximation of the optimality system. Rigorous improved a posteriori error bounds are derived and used to prove convergence of the resulting NCD-corrected adaptive Trust-Region Reduced Basis algorithm. Numerical experiments demonstrate that this approach enables to reduce the computational demand for large scale or multi-scale PDE constrained optimization problems significantly.
Funder
Deutsche Forschungsgemeinschaft
Subject
Applied Mathematics,Modeling and Simulation,Numerical Analysis,Analysis,Computational Mathematics
Cited by
9 articles.
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