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arXiv · 2303.04746

Necessary and sufficient conditions for multiple objective optimal regression designs

Lucy L. Gao·Jane J. Ye·Shangzhi Zeng·Julie Zhou
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Abstract

We typically construct optimal designs based on a single objective function. To better capture the breadth of an experiment's goals, we could instead construct a multiple objective optimal design based on multiple objective functions. While algorithms have been developed to find multi-objective optimal designs (e.g. efficiency-constrained and maximin optimal designs), it is far less clear how to verify the optimality of a solution obtained from an algorithm. In this paper, we provide theoretical results characterizing optimality for efficiency-constrained and maximin optimal designs on a discrete design space. We demonstrate how to use our results in conjunction with linear programming algorithms to verify optimality.

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Lucy L. Gao, Jane J. Ye, Shangzhi Zeng, Julie Zhou. 2023-03-08. Necessary and sufficient conditions for multiple objective optimal regression designs. https://arxiv.org/abs/2303.04746

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