Interior point method in tensor optimal transport

TL;DR

This paper develops an interior point method for tensor optimal transport problems involving multiple discrete measures, providing a new algorithmic approach with iteration complexity analysis.

Contribution

It introduces an interior point method with a barrier function for tensor optimal transport, including iteration bounds and convergence analysis.

Findings

Proposed an interior point method for d-TOT problems.

Provided iteration complexity estimates for the algorithm.

Analyzed convergence within epsilon precision.

Abstract

We study a tensor optimal transport (TOT) problem for $d\ge 2$ discrete measures. This is a linear programming problem on $d$-tensors. We introduces an interior point method (ipm) for $d$-TOT with a corresponding barrier function. Using a "short-step" ipm following central path within $\varepsilon$ precision we estimate the number of iterations.