Quantitative stability analysis of optimal solutions in PDE-constrained optimization

Authors:
Kerstin Brandes;Roland Griesse
Affiliations:
Lehrstuhl für Ingenieurmathematik, University of Bayreuth, Universitätsstraíe 30, D-95440 Bayreuth, Germany;Johann Radon Institute for Computational and Applied Mathematics (RICAM), Austrian Academy of Sciences, Altenbergerstraíe 69, A-4040 Linz, Austria
Venue:
Journal of Computational and Applied Mathematics
Year:
2007

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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.