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

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,...

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Bibliographic Details
Published in:Mathematics (Basel) Vol. 11; no. 4; p. 854
Main Author: Duarte, Belmiro P. M.
Format: Journal Article
Language:English
Published: Basel MDPI AG 01.02.2023
Subjects:
Algorithms
Convex analysis
Design of experiments
Design optimization
Equivalence
exact designs
Factorial experiments
Generalized linear models
Linear programming
Mathematical programming
Mixed integer
mixed-integer semidefinite programming
model-based optimal designs
Optimization
Optimization algorithms
Semidefinite programming
Split-plot design
ISSN:2227-7390, 2227-7390
Online Access:Get full text
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Summary: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.
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ISSN:2227-7390
2227-7390
DOI:10.3390/math11040854