Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2406.01541 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916271706079232 |
|---|---|
| author | Schmid, Jochen Seufert, Philipp Bortz, Michael |
| author_facet | Schmid, Jochen Seufert, Philipp Bortz, Michael |
| contents | We develop adaptive discretization algorithms for locally optimal experimental design of nonlinear prediction models. With these algorithms, we refine and improve a pertinent state-of-the-art algorithm in various respects. We establish novel termination, convergence, and convergence rate results for the proposed algorithms. In particular, we prove a sublinear convergence rate result under very general assumptions on the design criterion and, most notably, a linear convergence result under the additional assumption that the design criterion is strongly convex and the design space is finite. Additionally, we prove the finite termination at approximately optimal designs, including upper bounds on the number of iterations until termination. And finally, we illustrate the practical use of the proposed algorithms by means of two application examples from chemical engineering: one with a stationary model and one with a dynamic model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_01541 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Adaptive discretization algorithms for locally optimal experimental design Schmid, Jochen Seufert, Philipp Bortz, Michael Optimization and Control Statistics Theory We develop adaptive discretization algorithms for locally optimal experimental design of nonlinear prediction models. With these algorithms, we refine and improve a pertinent state-of-the-art algorithm in various respects. We establish novel termination, convergence, and convergence rate results for the proposed algorithms. In particular, we prove a sublinear convergence rate result under very general assumptions on the design criterion and, most notably, a linear convergence result under the additional assumption that the design criterion is strongly convex and the design space is finite. Additionally, we prove the finite termination at approximately optimal designs, including upper bounds on the number of iterations until termination. And finally, we illustrate the practical use of the proposed algorithms by means of two application examples from chemical engineering: one with a stationary model and one with a dynamic model. |
| title | Adaptive discretization algorithms for locally optimal experimental design |
| topic | Optimization and Control Statistics Theory |
| url | https://arxiv.org/abs/2406.01541 |