Quantitative stability analysis of optimal solutions in PDE-constrained optimization |
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Authors: | Kerstin Brandes Roland Griesse |
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Institution: | 1. Lehrstuhl für Ingenieurmathematik, University of Bayreuth, Universitätsstraße 30, D–95440 Bayreuth, Germany;2. Johann Radon Institute for Computational and Applied Mathematics (RICAM), Austrian Academy of Sciences, Altenbergerstraße 69, A–4040 Linz, Austria |
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Abstract: | PDE-constrained optimization problems under the influence of perturbation parameters are considered. A quantitative stability analysis for local optimal solutions is performed. The perturbation directions of greatest impact on an observed quantity are characterized using the singular value decomposition of a certain linear operator. An efficient numerical method is proposed to compute a partial singular value decomposition for discretized problems, with an emphasis on infinite-dimensional parameter and observation spaces. Numerical examples are provided. |
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Keywords: | 49K40 65F15 90C31 |
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