D-optimal designs via a cocktail algorithm

A "cocktail algorithm" is proposed for numerical computation of (approximate) D-optimal designs. This new algorithm extends the multiplicative algorithm of Silvey et al. (1978) and the vertex exchange method (VEM) of Bohning (1986), and shares their simplicity and monotonic convergence properties. Numerical examples show that the cocktail algorithm can lead to dramatically improved speed, sometimes by orders of magnitude, relative to either VEM or the multiplicative algorithm. Key to the improved speed is a new nearest neighbor exchange strategy, which acts locally and complements the global effect of the multiplicative algorithm. Possible extensions to related problems such as nonparametric maximum likelihood estimation are mentioned.