D-optimal designs via a cocktail algorithm

TL;DR

The paper introduces a fast, efficient algorithm called the cocktail algorithm for computing D-optimal experimental designs, significantly outperforming existing methods in speed through a novel local exchange strategy.

Contribution

It presents a new cocktail algorithm that extends existing methods, achieving faster convergence and improved computational efficiency for D-optimal design computation.

Findings

Significantly faster convergence compared to existing algorithms

Effective local exchange strategy enhances speed

Numerical examples demonstrate orders of magnitude improvement

Abstract

A fast new algorithm is proposed for numerical computation of (approximate) D-optimal designs. This "cocktail algorithm" extends the well-known vertex direction method (VDM; Fedorov 1972) and the multiplicative algorithm (Silvey, Titterington and Torsney, 1978), 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 the multiplicative algorithm or the vertex exchange method (a variant of VDM). 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.