多目标最优回归设计的充要条件
Necessary and sufficient conditions for multiple objective optimal regression designs
摘要：
我们通常基于单个目标函数构造最优设计。为了更好地捕捉实验目标的广度，我们可以基于多个目标函数构建多目标优化设计。虽然已经开发了算法来找到多目标最优设计（例如效率约束和最小最优设计），但如何验证从算法获得的解决方案的最优性还不太清楚。在本文中，我们提供的理论结果表征最优性的效率约束和最大最优设计的离散设计空间。我们演示了如何使用我们的结果结合线性规划算法来验证最优性。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
