Compound optimal design of experiments -- semidefinite programming formulations

Duarte, Belmiro P.M., Atkinson, Anthony C. and Oliveira, Nuno M.C (2025) Compound optimal design of experiments -- semidefinite programming formulations. Optimization and Engineering. ISSN 1389-4420 (In Press)

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Abstract

An optimal experimental design represents a structured approach to collecting data with the aim of maximizing the information gleaned. Achieving this requires defining an optimality criterion tailored to the specific model under consideration and the purpose of the investigation. However, it is often observed that a design optimized for one criterion may not perform optimally when applied to another. To mitigate this, one strategy involves employing compound designs. These designs balance multiple criteria to create robust experimental plans that are versatile across different applications. In our study, we systematically tackle the challenge of constructing compound approximate optimal experimental designs using Semidefinite Programming.We focus on discretized design spaces, with the objective function being the geometric or the arithmetic mean of design efficiencies relative to individual criteria.We address two combinations of two criteria: concave-concave (illustrated by DE–optimality) and convex-concave (such as DA–optimality). To handle the latter, we reformulate the problem as a bilevel problem. Here, the outer problem is solved using Surrogate Based Optimization, while the inner problem is addressed with a Semidefinite Programming solver. We demonstrate our formulations using both linear and nonlinear models (for the response) of the Beta class, previously linearized to facilitate analysis and comparison.

Item Type:	Article
Additional Information:	© 2025 The Author(s)
Divisions:	Statistics
Subjects:	H Social Sciences > HA Statistics T Technology > TA Engineering (General). Civil engineering (General)
Date Deposited:	27 May 2025 08:42
Last Modified:	27 May 2025 08:42
URI:	http://eprints.lse.ac.uk/id/eprint/128170

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