Abstract We propose a class of subspace ascent methods for computing optimal approximate designs that covers existing algorithms as well as new and more efficient ones. Within this class of methods, we construct a simple, randomized exchange algorithm (REX). Numerical comparisons suggest that the performance of REX is comparable or superior to that of state-of-the-art methods across a broad range of problem structures and sizes. We focus on the most commonly used criterion of D-optimality, which also has applications beyond experimental design, such as the construction of the minimum-volume ellipsoid containing a given set of data points. For D-optimality, we prove that the proposed algorithm converges to the optimum. We also provide formulas for the optimal exchange of weights in the case of the criterion of A-optimality, which enable one to use REX and some other algorithms for computing A-optimal and I-optimal designs. Supplementary materials for this article are available online.

中文翻译：

---

一种用于计算最佳近似实验设计的随机交换算法

摘要 我们提出了一类用于计算最优近似设计的子空间上升方法，这些方法涵盖了现有算法以及新的和更有效的算法。在此类方法中，我们构建了一个简单的随机交换算法 (REX)。数值比较表明，在广泛的问题结构和规模上，REX 的性能与最先进的方法相当或更好。我们专注于最常用的 D 最优性标准，它也有超出实验设计的应用，例如包含一组给定数据点的最小体积椭球的构建。对于 D 最优性，我们证明了所提出的算法收敛到最优。我们还提供了在 A 最优性标准的情况下优化权重交换的公式，这使人们能够使用 REX 和其他一些算法来计算 A 最优和 I 最优设计。本文的补充材料可在线获取。