Related papers: Quadratic optimal transportation problem with a po…
Optimal maps, solutions to the optimal transportation problems, are completely determined by the corresponding c-convex potential functions. In this paper, we give simple sufficient conditions for a smooth function to be c-convex when the…
Quantum optimal transportation seeks an operator which minimizes the total cost of transporting a quantum state to another state, under some constraints that should be satisfied during transportation. We formulate this issue by extending…
This paper considers the decentralized (discrete) optimal transport (D-OT) problem. In this setting, a network of agents seeks to design a transportation plan jointly, where the cost function is the sum of privately held costs for each…
For probability measures on a complete separable metric space, we present sufficient conditions for the existence of a solution to the Kantorovich transportation problem. We also obtain sufficient conditions (which sometimes also become…
This article generalizes the study of ramified optimal transport with capacity constraint in transport multi-paths by generalizing the $\mathbf{M}_{\alpha}$ cost to $\mathbf{M}_{\alpha,c}$, which incorporates capacity constraints into the…
Classical optimal transport problem seeks a transportation map that preserves the total mass betwenn two probability distributions, requiring their mass to be the same. This may be too restrictive in certain applications such as color or…
We propose a discrete time formulation of the semi martingale optimal transport problembased on multi-marginal entropic transport. This approach offers a new way to formulate and solve numerically the calibration problem proposed by Guo et…
One of the most impressive applications of a quantum annealer was optimizing a group of Volkswagen to reduce traffic congestion using a D-Wave system. A simple formulation of a quadratic term was proposed to reduce traffic congestion. This…
Given a positive l.s.c. convex function $\mathtt c : \mathbb R^d \to \mathbb R^d$ and an optimal transference plane $\underline{\pi}$ for the transportation problem \begin{equation*} \int \mathtt c(x'-x) \pi(dxdx'), \end{equation*} we show…
We consider the optimal transport problem over convex costs arising from optimal control of linear time-invariant(LTI) systems when the initial and target measures are assumed to be supported on the set of equilibrium points of the LTI…
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…
We study multi-marginal optimal transport problems from a probabilistic graphical model perspective. We point out an elegant connection between the two when the underlying cost for optimal transport allows a graph structure. In particular,…
Let $R$ and $B$ be two point sets in $\mathbb{R}^d$, with $|R|+ |B| = n$ and where $d$ is a constant. Next, let $\lambda : R \cup B \to \mathbb{N}$ such that $\sum_{r \in R } \lambda(r) = \sum_{b \in B} \lambda(b)$ be demand functions over…
We consider the multiple quantile hedging problem, which is a class of partial hedging problems containing as special examples the quantile hedging problem (F{\"o}llmer \& Leukert 1999) and the PnL matching problem (introduced in Bouchard…
The question of which costs admit unique optimizers in the Monge-Kantorovich problem of optimal transportation between arbitrary probability densities is investigated. For smooth costs and densities on compact manifolds, the only known…
Building on the results of Ma, Trudinger and Wang \cite{MTW}, and of the author \cite{L5}, we study two problems of optimal transportation on the sphere: the first corresponds to the cost function $d^2(x,y)$, where $d(\cdot,\cdot)$ is the…
It is well-known that plug-in statistical estimation of optimal transport suffers from the curse of dimensionality. Despite recent efforts to improve the rate of estimation with the smoothness of the problem, the computational complexity of…
There are interesting extensions of the problem of determining a joint probability with known marginals. On the one hand, one may impose size constraints on the joint probabilities. On the other, one may impose additional constraints like…
We provide a unifying interpretation of various optimal transport problems as a minimisation of a linear functional over the set of all Choquet representations of a given pair of probability measures ordered with respect to a certain convex…
We consider an optimal transport problem between laws of random probability measures: given a base cost function, we build the associated OT cost between probability measures that in turn we use to define the OT cost between probability…