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

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.