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

Abstract

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 a monotonicity 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 special cases. We provide numerical results demonstrating the efficiency of the proposed methods and discuss several extensions to other optimality criteria.