Improving updating rules in multiplicativealgorithms for computing D-optimal designs - Holger Dette; Andrey Pepelyshev; Anatoly Zhigljavsky (Universität Dortmund, Sonderforschungsbereich 475 - Komplexitätsreduktion in Multivariaten Datenstrukturen, 2007)
In this paper we discuss a class of multiplicative algorithms for computing D-optimal designs for regression models on a finite design space. We prove amonotonicity result for a sequence of determinants obtained by the iterations,and as a consequence the procedure yields a sequence of designs converging to the D-optimal design. The class of algorithms is indexed by a real parameter and contains two algorithms considered by Titterington (1976, 1978) as specialcases. We provide numerical results demonstrating the efficiency of the proposed methods and discuss several extensions to other optimality criteria.
Keywords: 519; D-optimal design; finite design space; multiplicative algorithm; minimal covering ellipsoid; Regression; Heuristisches Verfahren; Robustes Verfahren; Theorie