An adaptive discretization algorithm for locally optimal experimental design with constraints
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866914492435136512 |
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| author | Schmid, Jochen Seufert, Philipp Schwientek, Jan Seidel, Tobias Küfer, Karl-Heinz |
| author_facet | Schmid, Jochen Seufert, Philipp Schwientek, Jan Seidel, Tobias Küfer, Karl-Heinz |
| contents | We develop a novel iterative algorithm for locally optimal experimental design under constraints, like budget or performance constraints. It is an adaptive discretization algorithm. In every iteration, a discretized version of the constrained-design problem is solved and then the discretization is adaptively refined by adding an approximate violator of a suitable sufficient $\eps$-optimality condition for the current design. We prove that with $\eps = 0$, our algorithm converges to an optimal design and that with $\eps > 0$, our algorithm finitely terminates at an $\eps$-optimal design. Compared to the existing algorithms on constrained experimental design, our algorithm comes with considerably less computational effort because the nonlinear subproblems in our algorithm have a smaller dimension and have to be solved only approximately and only in selected iterations (typically the last few). Additionally, our algorithm covers a considerably larger class of constraints. We demonstrate the good convergence properties of the algorithm on experimental design problems from chemical engineering that feature time and yield constraints. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_18511 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | An adaptive discretization algorithm for locally optimal experimental design with constraints Schmid, Jochen Seufert, Philipp Schwientek, Jan Seidel, Tobias Küfer, Karl-Heinz Optimization and Control We develop a novel iterative algorithm for locally optimal experimental design under constraints, like budget or performance constraints. It is an adaptive discretization algorithm. In every iteration, a discretized version of the constrained-design problem is solved and then the discretization is adaptively refined by adding an approximate violator of a suitable sufficient $\eps$-optimality condition for the current design. We prove that with $\eps = 0$, our algorithm converges to an optimal design and that with $\eps > 0$, our algorithm finitely terminates at an $\eps$-optimal design. Compared to the existing algorithms on constrained experimental design, our algorithm comes with considerably less computational effort because the nonlinear subproblems in our algorithm have a smaller dimension and have to be solved only approximately and only in selected iterations (typically the last few). Additionally, our algorithm covers a considerably larger class of constraints. We demonstrate the good convergence properties of the algorithm on experimental design problems from chemical engineering that feature time and yield constraints. |
| title | An adaptive discretization algorithm for locally optimal experimental design with constraints |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2604.18511 |