An Integer Program for Pricing Support Points of Exact Barycenters

Abstract

The ideas presented in this paper represent the most recent progress in a multiyear effort to create a practical computational algorithm for computing exact barycenters. We began by exploring linear programming formulations based on the underlying structure of the input measures (published in INFORMS Optimization in 2020). Since then, we explored the use of column generation methods, which led to significant computational improvements, but cannot overcome the underlying exponentiality of the problem as the dimension grows. However, through a shift of this difficulty to a separate pricing problem, now taking the form of a mixed-integer program, we arrived at the most competitive column generation approach for the dynamic generation of exact support points in higher dimensions.