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An Optimization Perspective on the Monotonicity of the Multiplicative Algorithm for Optimal Experimental Design
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An Optimization Perspective on the Monotonicity of the Multiplicative Algorithm for Optimal Experimental Design

Renbo Zhao
ArXiv.org
Cornell University
08/09/2025
DOI: 10.48550/arxiv.2508.07074
url
https://doi.org/10.48550/arxiv.2508.07074View
Preprint (Author's original)This preprint has not been evaluated by subject experts through peer review. Preprints may undergo extensive changes and/or become peer-reviewed journal articles. Open Access

Abstract

We provide an optimization-based argument for the monotonicity of the multiplicative algorithm (MA) for a class of optimal experimental design problems considered in Yu (2010). Our proof avoids introducing auxiliary variables (or problems) and leveraging statistical arguments, and is much more straightforward and simpler compared to the proof in Yu (2010). The simplicity of our monotonicity proof also allows us to easily identify several sufficient conditions that ensure the strict monotonicity of MA. In addition, we provide two simple and similar-looking examples on which MA behaves very differently. These examples offer insight in the behaviors of MA, and also reveal some limitations of MA when applied to certain optimality criteria. We discuss these limitations, and pose open problems that may lead to deeper understanding of the behaviors of MA on these optimality criteria.
Mathematics - Optimization and Control

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