Improvements on removing non-optimal support points in D-optimum design algorithms
We improve the inequality used in (Pronzato, 2003) to remove points from the design space during the search for a $D$-optimum design, which can be used to accelerate design algorithms. Let $\xi$ be any design on a compact space $\mathcal{X} \subset \mathbb{R}^m$ with a nonsingular information matrix, and let $m+\epsilon$ be the maximum of the variance function $d(\xi,\mathbf{x})$ over all $\mathbf{x} \in \mathcal{X}$. We prove that any support point $\mathbf{x}_{*}$ of a $D$-optimum design on $\mathcal{X}$ must satisfy the inequality $d(\xi,\mathbf{x}_{*}) \geq m(1+\epsilon/2-\sqrt{\epsilon(4+\epsilon-4/m)}/2)$. We show that this new lower bound on $d(\xi,\mathbf{x}_{*})$ is, in a sense, the best possible.