We establish strong connections between two fundamental nonlinear 0/1 optimization problems coming from the area of experimental design, namely maximum entropy sampling and 0/1 D-Optimality. The connections are based on maps between instances, and we analyze the behavior of these maps. Using these maps, we transport basic upper-bounding methods between these two problems, and we are able to establish new domination results and other inequalities relating various basic upper bounds. Further, we establish results relating how different branch-and-bound schemes based on these maps compare. Additionally, we observe some surprising numerical results, where bounding methods that did not seem promising in their direct application to real-data MESP instances, are now useful for MESP instances that come from 0/1 D-Optimality.

翻译：本文建立了实验设计领域中两个基础非线性0/1优化问题——最大熵抽样与0/1 D最优性——之间的紧密联系。这些联系基于实例间的映射关系，我们分析了这些映射的性质。利用这些映射，我们在两个问题间转移基本的上界方法，从而建立了新的支配关系以及关联各类基本上界的不等式。此外，我们研究了基于这些映射的不同分支定界方案的比较结果。值得注意的是，我们观察到一些令人惊讶的数值结果：某些上界方法在直接应用于实际数据的MESP实例时效果有限，但对于源自0/1 D最优性的MESP实例却具有实用价值。