相关论文: Solution of the Probabilistic Lambert's Problem: O…

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…

The \emph{Schr\"odinger problem} is obtained by replacing the mean square distance with the relative entropy in the Monge-Kantorovich problem. It was first addressed by Schr\"odinger as the problem of describing the most likely evolution of…

The Schr\"odinger bridge problem (SBP) is gaining increasing attention in generative modeling and showing promising potential even in comparison with the score-based generative models (SGMs). SBP can be interpreted as an entropy-regularized…

The subject of this work has its roots in the so called Schroedginer Bridge Problem (SBP) which asks for the most likely distribution of Brownian particles in their passage between observed empirical marginal distributions at two distinct…

We investigate the martingale Schr\"odinger bridge, recently introduced by Nutz and Wiesel as a distinguished martingale transport plan between two probability measures in convex order. We show that this construction extends naturally to…

To remedy the drawbacks of full-mass or fixed-mass constraints in classical optimal transport, we propose adaptive optimal transport which is distinctive from the classical optimal transport in its ability of adaptive-mass preserving. It…

We consider an optimal transport problem on the unit simplex whose solutions are given by gradients of exponentially concave functions and prove two main results. First, we show that the optimal transport is the large deviation limit of a…

We propose a numerical algorithm for the computation of multi-marginal optimal transport (MMOT) problems involving general probability measures that are not necessarily discrete. By developing a relaxation scheme in which marginal…

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…

We consider network routing under random link failures with a desired final distribution. We provide a mathematical formulation of a relaxed transport problem where the final distribution only needs to be close to the desired one. The…

We consider the problem to identify the most likely flow in phase space, of (inertial) particles under stochastic forcing, that is in agreement with spatial (marginal) distributions that are specified at a set of points in time. The…

The optimal (Monge-Kantorovich) transportation problem is discussed from several points of view. The Lagrangian formulation extends the action of the {\em Lagrangian} $L(v,x,t)$ from the set of orbits in $\R^n$ to a set of measure-valued…

In this paper, we present a numerical method, based on iterative Bregman projections, to solve the optimal transport problem with Coulomb cost. This is related to the strong interaction limit of Density Functional Theory. The first idea is…

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 problem to steer a linear dynamical system with full state observation from an initial gaussian distribution in state-space to a final one with minimum energy control. The system is stochastically driven through the control…

We study a rather general class of optimal "ballistic" transport problems for matrix-valued measures. These problems naturally arise, in the spirit of \emph{Y. Brenier. Comm. Math. Phys. (2018) 364(2) 579-605}, from a certain dual…

The orbital boundary value problem, also known as Lambert Problem, is revisited. Building upon Lancaster and Blanchard approach, new relations are revealed and a new variable representing all problem classes, under L-similarity, is used to…

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…

A method is presented to solve a stochastic, nonlinear optimal control problem representative of spacecraft trajectory design under uncertainty. The problem is reformulated as a chance constrained nonlinear program, or what is known as a…

In this work, we develop a collection of novel methods for the entropic-regularised optimal transport problem, which are inspired by existing mirror descent interpretations of the Sinkhorn algorithm used for solving this problem. These are…