Title: A differentiable reformulation for E-optimal design of experiments in nonlinear dynamic biosystems
Authors: Telen, Dries ×
Van Riet, Nick
Logist, Filip
Van Impe, Jan #
Issue Date: Jun-2015
Publisher: Elsevier
Series Title: Mathematical Biosciences vol:264 pages:1-7
Abstract: Informative experiments are highly valuable for estimating parameters in nonlinear dynamic bioprocesses. Techniques for optimal experiment design ensure the systematic design of such informative experiments. The E-criterion which can be used as objective function in optimal experiment design requires the maximization of the smallest eigenvalue of the Fisher information matrix. However, one problem with the minimal eigenvalue function is that it can be nondifferentiable. In addition, no closed form expression exists for the computation of eigenvalues of a matrix larger than a 4 by 4 one. As eigenvalues are normally computed with iterative methods, state-of-the-art optimal control solvers are not able to exploit automatic differentiation to compute the derivatives with respect to the decision variables. In the current paper a reformulation strategy from the field of convex optimization is suggested to circumvent these difficulties. This reformulation requires the inclusion of a matrix inequality constraint involving positive semidefiniteness. In this paper, this positive semidefiniteness constraint is imposed via Sylverster’s criterion. As a result the maximization of the minimum eigenvalue function can be formulated in standard optimal control solvers through the addition of nonlinear constraints. The presented methodology is successfully illustrated with a case study from the field of predictive microbiology.
ISSN: 0025-5564
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Bio- & Chemical Systems Technology, Reactor Engineering and Safety Section
Sustainable Chemical Process Technology TC, Technology Campus De Nayer Sint-Katelijne-Waver
Sustainable Chemical Process Technology TC
× corresponding author
# (joint) last author

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