Necessary and sufficient conditions for multiple objective optimal regression designs
Methodology
2023-03-09 v1
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.
Cite
@article{arxiv.2303.04746,
title = {Necessary and sufficient conditions for multiple objective optimal regression designs},
author = {Lucy L. Gao and Jane J. Ye and Shangzhi Zeng and Julie Zhou},
journal= {arXiv preprint arXiv:2303.04746},
year = {2023}
}