Exact Optimal Designs of Experiments for Factorial Models via Mixed-Integer Semidefinite Programming

Belmiro P. M. Duarte ()
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Belmiro P. M. Duarte: Department of Chemical and Biological Engineering, Coimbra Engineering Academia, Polytechnic Institute of Coimbra, Rua Pedro Nunes, Quinta da Nora, 3030-199 Coimbra, Portugal

Mathematics, 2023, vol. 11, issue 4, 1-17

Abstract: The systematic design of exact optimal designs of experiments is typically challenging, as it results in nonconvex optimization problems. The literature on the computation of model-based exact optimal designs of experiments via mathematical programming, when the covariates are categorical variables, is still scarce. We propose mixed-integer semidefinite programming formulations, to find exact D-, A- and I-optimal designs for linear models, and locally optimal designs for nonlinear models when the design domain is a finite set of points. The strategy requires: (i) the generation of a set of candidate treatments; (ii) the formulation of the optimal design problem as a mixed-integer semidefinite program; and (iii) its solution, employing appropriate solvers. For comparison, we use semidefinite programming-based formulations to find equivalent approximate optimal designs. We demonstrate the application of the algorithm with various models, considering both unconstrained and constrained setups. Equivalent approximate optimal designs are used for comparison.

Keywords: factorial experiments; exact designs; mixed-integer semidefinite programming; model-based optimal designs (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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