Published on Mon Feb 15 2021

Relaxation of optimal transport problem via strictly convex functions

Asuka Takatsu

An optimal transport problem on finite spaces is a linear program. This paper provides the mathematical foundations and an iterative process based on a gradient descent.

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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.