Relaxation of optimal transport problem via strictly convex functions

2021/02/15 by Takatsu, Asuka
#49Q22 #90C25 #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (stat.ML) #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.2102.07336

Abstract

An optimal transport problem on finite spaces is a linear program. Recently, a relaxation of the optimal transport problem via strictly convex functions, especially via the Kullback--Leibler divergence, sheds new light on data sciences. This paper provides the mathematical foundations and an iterative process based on a gradient descent for the relaxed optimal transport problem via Bregman divergences.

Related

• Convex duality in nonlinear optimal transport
• A strategy for non-strictly convex transport costs and the example of ||x-y||p in R2
• Applications of optimal transport methods in the least gradient problem
• Optimal transport problems regularized by generic convex functions: A geometric and algorithmic approach
• Iterative Bregman Projections for Regularized Transportation Problems