Computing T-optimal designs via nested semi-infinite programming and twofold adaptive discretization

David Mogalle (), Philipp Seufert, Jan Schwientek, Michael Bortz and Karl-Heinz Küfer
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David Mogalle: Fraunhofer Institute for Industrial Mathematics (ITWM)
Philipp Seufert: Fraunhofer Institute for Industrial Mathematics (ITWM)
Jan Schwientek: Fraunhofer Institute for Industrial Mathematics (ITWM)
Michael Bortz: Fraunhofer Institute for Industrial Mathematics (ITWM)
Karl-Heinz Küfer: Fraunhofer Institute for Industrial Mathematics (ITWM)

Computational Statistics, 2024, vol. 39, issue 5, No 3, 2478 pages

Abstract: Abstract Modelling real processes often results in several suitable models. In order to be able to distinguish, or discriminate, which model best represents a phenomenon, one is interested, e.g., in so-called T-optimal designs. These consist of the (design) points from a generally continuous design space at which the models deviate most from each other under the condition that they are best fitted to those points. Thus, the T-criterion represents a bi-level optimization problem, which can be transferred into a semi-infinite one but whose solution is very unstable or time consuming for non-linear models and non-convex lower- and upper-level problems. If one considers only a finite number of possible design points, a numerically well tractable linear semi-infinite optimization problem arises. Since this is only an approximation of the original model discrimination problem, we propose an algorithm which alternately and adaptively refines discretizations of the parameter as well as of the design space and, thus, solves a sequence of linear semi-infinite programs. We prove convergence of our method and its subroutine and show on the basis of discrimination tasks from process engineering that our approach is stable and can outperform the known methods.

Keywords: Model discrimination; Multi-level optimization; Semi-infinite optimization; Adaptive discretization; Global optimization; Bio- and chemical process engineering (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s00180-023-01370-4

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