1811. Optimizing Multi-Response Experimental Designs under Linear Constraints
Invited abstract in session WC-15: Topics in Combinatorial Optimization 1, stream Combinatorial Optimization.
Wednesday, 12:30-14:00Room: Esther Simpson 1.08
Authors (first author is the speaker)
| 1. | Pál Somogyi
|
| Department of Applied Mathematics and Statistics, Faculty of Mathematics, Physics and Informatics; Comenius University Bratislava |
Abstract
Optimal experimental design is a combinatorial optimization problem that seeks to select experimental conditions to maximize the information obtained from an experiment, thereby enabling the estimation of unknown parameters with minimal variance. Since optimal design problems are NP-hard, they are often addressed using heuristics or approximations, such as continuous relaxation, known as approximate optimal design.
Harman et al. (J Am Stat Assoc 115:529, 2020) introduced a simple and efficient algorithm, REX, to solve the approximate optimal design problem. However, this algorithm is limited to basic optimality criteria and rank-one elementary information matrices (EIMs). Somogyi et al. (preprint, arXiv:2407.16283, 2024) extended REX for multi-response models (mREX), generalizing it to all Kiefer’s optimality criteria and EIMs of any rank.
In this contribution, we present the mREX algorithm and we propose a nontrivial extension of this algorithm to handle linear constraints (e.g., on financial resources, materials or time). We present two approaches: (i) transforming the constrained problem into an equivalent problem with EIMs of any rank, and (ii) fully extending the mREX algorithm to directly incorporate linear constraints. Numerical results demonstrate the stability and convergence of the proposed methods.
Keywords
- Algorithms
- Convex Optimization
- Programming, Constraint
Status: accepted
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