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A branch-and-bound algorithm for the exact optimal experimental design problem

A branch-and-bound algorithm for the exact optimal experimental design problem
A branch-and-bound algorithm for the exact optimal experimental design problem

We discuss a generalisation of the approximate optimal experimental design problem, in which the weight of each regression point needs to stay in a closed interval. We work with Kiefer’s optimality criteria which include the well-known D- and A-optimality as special cases. We propose a first-order algorithm for the generalised problem that redistributes the weights of two regression points in each iteration. We develop a branch-and-bound algorithm for exact optimal experimental design problems under Kiefer’s criteria where the subproblems in the search tree are equivalent to the generalized approximate design problem, and therefore, can be solved efficiently by the first-order method. We observe that our branch-and-bound algorithm is favourable to a popular exchange heuristic for certain problem instances.

A-optimality, D-optimality, Exact optimal experimental design, Kiefer’s optimality criteria
0960-3174
Ahipaşaoğlu, Selin Damla
d69f1b80-5c05-4d50-82df-c13b87b02687
Ahipaşaoğlu, Selin Damla
d69f1b80-5c05-4d50-82df-c13b87b02687

Ahipaşaoğlu, Selin Damla (2021) A branch-and-bound algorithm for the exact optimal experimental design problem. Statistics and Computing, 31 (5), [65]. (doi:10.1007/s11222-021-10043-5).

Record type: Article

Abstract

We discuss a generalisation of the approximate optimal experimental design problem, in which the weight of each regression point needs to stay in a closed interval. We work with Kiefer’s optimality criteria which include the well-known D- and A-optimality as special cases. We propose a first-order algorithm for the generalised problem that redistributes the weights of two regression points in each iteration. We develop a branch-and-bound algorithm for exact optimal experimental design problems under Kiefer’s criteria where the subproblems in the search tree are equivalent to the generalized approximate design problem, and therefore, can be solved efficiently by the first-order method. We observe that our branch-and-bound algorithm is favourable to a popular exchange heuristic for certain problem instances.

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More information

Accepted/In Press date: 10 August 2021
Published date: 27 August 2021
Keywords: A-optimality, D-optimality, Exact optimal experimental design, Kiefer’s optimality criteria

Identifiers

Local EPrints ID: 451670
URI: http://eprints.soton.ac.uk/id/eprint/451670
ISSN: 0960-3174
PURE UUID: c6c56f84-253b-43ac-8213-8fbb5ac87da6
ORCID for Selin Damla Ahipaşaoğlu: ORCID iD orcid.org/0000-0003-1371-315X

Catalogue record

Date deposited: 19 Oct 2021 16:31
Last modified: 10 Jan 2022 03:21

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