Weak Optimal Entropy Transport Problems

TL;DR

This paper introduces a new class of weak optimal entropy transport problems that unify existing transport models, establishes duality results, and extends to martingale variants with duality and homogeneous constraints.

Contribution

It proposes a unified framework for weak optimal entropy transport problems, including duality theory and martingale extensions, advancing the mathematical understanding of entropy-based transport models.

Findings

Established Kantorovich duality for weak optimal entropy transport.

Introduced martingale optimal entropy transport problems with duality.

Connected entropy transport problems with homogeneous constraints.

Abstract

In this paper, we introduce weak optimal entropy transport problems that cover both optimal entropy transport problems and weak optimal transport problems introduced by Liero, Mielke, and Savar\'{e} [27]; and Gozlan, Roberto, Samson and Tetali [20], respectively. Under some mild assumptions of entropy functionals, we establish a Kantorovich type duality for our weak optimal entropy transport problem. We also introduce martingale optimal entropy transport problems, and express them in terms of duality, homogeneous marginal perspective functionals and homogeneous constraints.