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Parameter estimation and optimum experimental design for differential equation models. (English) Zbl 1269.65014
Bock, Hans Georg (ed.) et al., Model based parameter estimation. Theory and applications. Based on the workshop on parameter estimation, Heidelberg, Germany, 2009. Berlin: Springer (ISBN 978-3-642-30366-1/hbk; 978-3-642-30367-8/ebook). Contributions in Mathematical and Computational Sciences 4, 1-30 (2013).
Summary: This article reviews state-of-the-art methods for parameter estimation and optimum experimental design in optimization based modeling. For the calibration of differential equation models for nonlinear processes, constrained parameter estimation problems are considered. For their solution, numerical methods based on the boundary value problem method optimization approach consisting of multiple shooting and a generalized Gauss-Newton method are discussed. To suggest experiments that deliver data to minimize the statistical uncertainty of parameter estimates, optimum experimental design problems are formulated, an intricate class of non-standard optimal control problems, and derivative-based methods for their solution are presented.
For the entire collection see [Zbl 1261.65002].

MSC:
65C60 Computational problems in statistics (MSC2010)
62F10 Point estimation
65L80 Numerical methods for differential-algebraic equations
65K10 Numerical optimization and variational techniques
49J15 Existence theories for optimal control problems involving ordinary differential equations
49M15 Newton-type methods
62K05 Optimal statistical designs
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