On the relationship between MESP and 0/1 D-Opt and their upper bounds

TL;DR

This paper explores the deep connections between maximum entropy sampling and 0/1 D-Optimality problems, establishing mappings that transfer bounds and improve understanding of their solution schemes.

Contribution

It introduces new mappings between MESP and 0/1 D-Optimality, enabling the transfer of upper bounds and comparison of branch-and-bound methods, revealing novel inequalities and insights.

Findings

Established new domination results for upper bounds

Transferred bounding methods between problems, improving bounds

Numerical results show unexpected usefulness of certain bounds

Abstract

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.