Improving updating rules in multiplicative algorithms for computing D-optimal designs

Authors:
Holger Dette;Andrey Pepelyshev;Anatoly Zhigljavsky
Affiliations:
Ruhr-Universität Bochum, Fakultät für Mathematik, 44780 Bochum, Germany;St. Petersburg State University, Department of Mathematics, St. Petersburg, Russia;Cardiff University, School of Mathematics, Cardiff CF24 4AG, UK
Venue:
Computational Statistics & Data Analysis
Year:
2008

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Abstract

A class of multiplicative algorithms for computing D-optimal designs for regression models on a finite design space is discussed and a monotonicity result for a sequence of determinants obtained by the iterations is proved. As a consequence the convergence of the sequence of designs to the D-optimal design is established. The class of algorithms is indexed by a real parameter and contains two algorithms considered previously as special cases. Numerical results are provided to demonstrate the efficiency of the proposed methods. Finally, several extensions to other optimality criteria are discussed.