Related papers: A non-linear monotonicity principle and applicatio…
We establish the stability of solutions to the entropically regularized optimal transport problem with respect to the marginals and the cost function. The result is based on the geometric notion of cyclical invariance and inspired by the…
A fundamental concept in optimal transport is c-cyclical monotonicity: it allows to link the optimality of transport plans to the geometry of their support sets. Recently, related concepts have been successfully applied in the…
We study the convergence of entropically regularized optimal transport to optimal transport. The main result is concerned with the convergence of the associated optimizers and takes the form of a large deviations principle quantifying the…
The optimal transport problem has recently developed into a powerful framework for various applications in estimation and control. Many of the recent advances in the theory and application of optimal transport are based on regularizing the…
This article studies problems of optimal transport, by embedding them in a general functional analytic framework of convex optimization. This provides a unified treatment of a large class of related problems in probability theory and allows…
This paper introduces a dynamic formulation of divergence-regularized optimal transport with weak targets on the path space. In our formulation, the classical relative entropy penalty is replaced by a general convex divergence, and terminal…
This paper focuses on martingale optimal transport problems when the martingales are assumed to have bounded quadratic variation. First, we give a result that characterizes the existence of a probability measure satisfying some convex…
This paper studies the geometry of the optimizer for the optimal transport problem with capacity constraints. We introduce the concept of c-capacity monotonicity, which is a generalization of c-cyclical monotonicity in optimal transport. We…
The classical problem of optimal transportation can be formulated as a linear optimization problem on a convex domain: among all joint measures with fixed marginals find the optimal one, where optimality is measured against a cost function.…
Monotonicity and convex analysis arise naturally in the framework of multi-marginal optimal transport theory. However, a comprehensive multi-marginal monotonicity and convex analysis theory is still missing. To this end we study extensions…
In optimal transport, quadratic regularization is a sparse alternative to entropic regularization: the solution measure tends to have small support. Computational experience suggests that the support decreases monotonically to the…
This paper exploit the equivalence between the Schr\"odinger Bridge problem and the entropy penalized optimal transport in order to find a different approach to the duality, in the spirit of optimal transport. This approach results in a…
We consider the inverse problems of for the fractional Schr\"odinger equation by using monotonicity formulas. We provide if-and-only-if monotonicity relations between positive bounded potentials and their associated nonlocal…
We introduce a new class of convex-regularized Optimal Transport losses, which generalizes the classical Entropy-regularization of Optimal Transport and Sinkhorn divergences, and propose a generalized Sinkhorn algorithm. Our framework…
We study the optimal transport between two probability measures on the real line, where the transport plans are laws of one-step martingales. A quasi-sure formulation of the dual problem is introduced and shown to yield a complete duality…
Weak optimal transport generalizes the classical theory of optimal transportation to nonlinear cost functions and covers a range of problems that lie beyond the traditional theory - including entropic transport, martingale transport, and…
We show continuity of the martingale optimal transport optimisation problem as a functional of its marginals. This is achieved via an estimate on the projection in the nested/causal Wasserstein distance of an arbitrary coupling on to the…
From the mathematical side, nonlinear Schr\"odinger equations are usually investigated via variational methods, that cease to work in higher dimensions. This thesis tries to overcome this problem by focusing on spherically symmetric…
We consider the problem of minimizing the entropy of a law with respect to the law of a reference branching Brownian motion under density constraints at an initial and final time. We call this problem the branching Schr\"odinger problem by…
Capacity constrained optimal transport is a variant of optimal transport, which adds extra constraints on the set of feasible couplings in the original optimal transport problem to limit the mass transported between each pair of source and…