Compound optimal design of experiments - semidefinite programming formulations

Belmiro P.M. Duarte, Anthony C. Atkinson and Nuno M.C Oliveira

LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library

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.

Keywords: compound optimal designs; semidefinite programming; concave-concave criteria; convex-concave criteria; surrogate based optimization (search for similar items in EconPapers)
JEL-codes: C1 (search for similar items in EconPapers)
Pages: 23 pages
Date: 2025-07-05
References: Add references at CitEc
Citations:

Published in Optimization and Engineering, 5, July, 2025. ISSN: 1389-4420

Downloads: (external link)
http://eprints.lse.ac.uk/128170/ Open access version. (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:ehl:lserod:128170

Access Statistics for this paper

More papers in LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library LSE Library Portugal Street London, WC2A 2HD, U.K.. Contact information at EDIRC.
Bibliographic data for series maintained by LSERO Manager ().