Strict Monotonicity and Convergence Rate of Titterington's Algorithm for Computing D-optimal Designs

TL;DR

This paper analyzes Titterington's multiplicative algorithm for D-optimal design, proving its strict monotonicity and deriving its convergence rate, which explains the improved convergence of certain modifications.

Contribution

It establishes strict monotonicity for Titterington's algorithm and derives a convergence rate formula, enhancing understanding of its efficiency and modifications.

Findings

Proves strict monotonicity of Titterington's algorithm.

Derives a formula for the convergence rate.

Explains why certain modifications converge faster.

Abstract

We study a class of multiplicative algorithms introduced by Silvey et al. (1978) for computing D-optimal designs. Strict monotonicity is established for a variant considered by Titterington (1978). A formula for the rate of convergence is also derived. This is used to explain why modifications considered by Titterington (1978) and Dette et al. (2008) usually converge faster.