相关论文: Matrix-valued Monge-Kantorovich Optimal Mass Trans…
The multistochastic $ (n,k)$-Monge--Kantorovich problem on a product space $\prod_{i=1}^n X_i$ is an extension of the classical Monge--Kantorovich problem. This problem is considered on the space of measures with fixed projections onto…
Let (X,L) be a (semi-) polarized complex projective variety and T a real torus acting holomorphically on X with moment polytope P. Given a probability density g on P we introduce a new type of Monge-Ampere measure on X, defined for singular…
We consider a class of convex optimization problems modelling temporal mass transport and mass change between two given mass distributions (the so-called dynamic formulation of unbalanced transport), where we focus on those models for which…
A simple procedure to map two probability measures in $\mathbb{R}^d$ is the so-called \emph{Knothe-Rosenblatt rearrangement}, which consists in rearranging monotonically the marginal distributions of the last coordinate, and then the…
The purpose of this note is to show that the solution to the Kantorovich optimal transportation problem is supported on a Lipschitz manifold, provided the cost is $C^{2}$ with non-singular mixed second derivative. We use this result to…
We propose a volumetric formulation for computing the Optimal Transport problem defined on surfaces in $\mathbb{R}^3$, found in disciplines like optics, computer graphics, and computational methodologies. Instead of directly tackling the…
In this paper we study theoretical properties of the entropy-transport functional with repulsive cost functions. We provide sufficient conditions for the existence of a minimizer in a class of metric spaces and prove 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…
The duality theory of the Monge--Kantorovich transport problem is analyzed in a general setting. The spaces $X, Y$ are assumed to be polish and equipped with Borel probability measures $\mu$ and $\nu$. The transport cost function $c:X\times…
We consider the simultaneous optimal transportation of measures, where the target marginal is not necessarily fixed. For this problem, we prove the existence of a solution for completely regular spaces and investigate the structure of the…
We investigate the transportation problem under a Monge cost structure and derive compact formulas for optimal dual solutions based on the northwest-corner rule. As an application illustrating how these formulas yield structural insight…
The purpose of this paper is to show that in a finite dimensional metric space with Alexandrov's curvature bounded below, Monge's transport problem for the quadratic cost admits a unique solution.
The optimal transport problem is studied in the context of Lorentz-Finsler geometry. For globally hyperbolic Lorentz-Finsler spacetimes the first Kantorovich problem and the Monge problem are solved. Further the intermediate regularity of…
In this paper, we study optimal transportation problems for multifractal random measures. Since these measures are much less regular than optimal transportation theory requires, we introduce a new notion of transportation which is…
The Monge-Kantorovich transportation problem involves optimizing with respect to a given a cost function. Uniqueness is a fundamental open question about which little is known when the cost function is smooth and the landscapes containing…
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…
In the field of optimal transport, two prominent subfields face each other: (i) unregularized optimal transport, "\`a-la-Kantorovich", which leads to extremely sparse plans but with algorithms that scale poorly, and (ii)…
In this work we study a modification of the Monge-Kantorovich problem taking into account path dependence and interaction effects between particles. We prove existence of solutions under mild conditions on the data, and after imposing…
This paper is devoted to variational problems on the set of probability measures which involve optimal transport between unequal dimensional spaces. In particular, we study the minimization of a functional consisting of the sum of a term…
By investigating model-independent bounds for exotic options in financial mathematics, a martingale version of the Monge-Kantorovich mass transport problem was introduced in \cite{BeiglbockHenry…