A non-conforming dual approach for adaptive Trust-Region reduced basis approximation of PDE-constrained parameter optimization
| Autor: | Tim Keil, Mario Ohlberger, Felix Schindler, Stefan Volkwein, Luca Mechelli |
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| Rok vydání: | 2021 |
| Předmět: |
Model order reduction
Numerical Analysis Trust region Mathematical optimization Basis (linear algebra) Applied Mathematics Constrained optimization Numerical Analysis (math.NA) 010103 numerical & computational mathematics Function (mathematics) 01 natural sciences 010101 applied mathematics Computational Mathematics Optimization and Control (math.OC) Modeling and Simulation Broyden–Fletcher–Goldfarb–Shanno algorithm Convergence (routing) FOS: Mathematics A priori and a posteriori Mathematics - Numerical Analysis 0101 mathematics Mathematics - Optimization and Control 49M20 49K20 35J20 65N30 90C06 Analysis Mathematics |
| Zdroj: | ESAIM: Mathematical Modelling and Numerical Analysis. 55:1239-1269 |
| ISSN: | 1290-3841 0764-583X |
| DOI: | 10.1051/m2an/2021019 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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