Certified PDE-constrained parameter optimization using reduced basis surrogate models for evolution problems

• Published in: Computational optimization and applications Vol. 60; no. 3; pp. 753 - 787
• Main Authors: Dihlmann, Markus A., Haasdonk, Bernard
• Format: Journal Article
• Language: English
• Published: Boston Springer US 01.04.2015; Springer Nature B.V
• Subjects: Advection-diffusion equation; Analysis; Computation; Computer science; Construction; Convex and Discrete Geometry; Cost engineering; Derivatives; Differential equations; Estimation bias; Estimators; Evolution; Management Science; Mathematical models; Mathematics; Mathematics and Statistics; Methods; Operations Research; Operations Research/Decision Theory; Operators; Optimization; Partial differential equations; Statistics; Studies; A-posteriori error estimation; Surrogate model; Parameter optimization; Reduced basis method; PDE-constrained optimization; Reduced order modeling

We consider parameter optimization problems which are subject to constraints given by parametrized partial differential equations. Discretizing this problem may lead to a large-scale optimization problem which can hardly be solved rapidly. In order to accelerate the process of parameter optimization...