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A Randomized Exchange Algorithm for Computing Optimal Approximate Designs of Experiments
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DOI：10.1080/01621459.2018.1546588.png)
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Abstract
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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. for this article are available online.
Keywords:
A-optimality
Convex optimization
D-optimality
I-optimality
Minimum-volume enclosing ellipsoid
Optimal approximate designs of experiments
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