Related papers: Optimal pricing for optimal transport
We study the entropic regularizations of optimal transport problems under suitable summability assumptions on the point-wise transport cost. These summability assumptions already appear in the literature. However, we show that the weakest…
We prove a central limit theorem for the entropic transportation cost between subgaussian probability measures, centered at the population cost. This is the first result which allows for asymptotically valid inference for entropic optimal…
We consider an optimization problem in a given region $Q$ where an agent has to decide the price $p(x)$ of a product for every $x\in Q$. The customers know the pricing pattern $p$ and may shop at any place $y$, paying the cost $p(y)$ and…
A result of Hohloch links the theory of integer partitions with the Monge formulation of the optimal transport problem, giving the optimal transport map between (Young diagrams of) integer partitions and their corresponding symmetric…
We study a generalization of the multi-marginal optimal transport problem, which has no fixed number of marginals $N$ and is inspired of statistical mechanics. It consists in optimizing a linear combination of the costs for all the possible…
The quadratically regularized optimal transport problem has recently been considered in various applications where the coupling needs to be \emph{sparse}, i.e., the density of the coupling needs to be zero for a large subset of the product…
The dual attainment 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:\XY…
We study optimal transportation with the quadratic cost function in geodesic metric spaces satisfying suitable non-branching assumptions. We introduce and study the notions of slope along curves and along geodesics and we apply the latter…
We introduce a new variant of the weak optimal transport problem where mass is distributed from one space to the other through unnormalized kernels. We give sufficient conditions for primal attainment and prove a dual formula for this…
We study a single-period optimal transport problem on $\mathbb{R}^2$ with a covariance-type cost function $c(x,y) = (x_1-y_1)(x_2-y_2)$ and a backward martingale constraint. We show that a transport plan $\gamma$ is optimal if and only if…
We propose an implicit neural formulation of optimal transport that eliminates adversarial min--max optimization and multi-network architectures commonly used in existing approaches. Our key idea is to parameterize a single potential in the…
We prove that $c$-cyclically monotone transport plans $\pi$ optimize the Monge-Kantorovich transportation problem under an additional measurability condition. This measurability condition is always satisfied for finitely valued, lower…
This chapter describes techniques for the numerical resolution of optimal transport problems. We will consider several discretizations of these problems, and we will put a strong focus on the mathematical analysis of the algorithms to solve…
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…
We analyze pricing mechanisms in electricity markets with AC power flow equations that define a nonconvex feasible set for the economic dispatch problem. Specifically, we consider two possible pricing schemes. The first among these prices…
According to the fundamental theorems of welfare economics, any competitive equilibrium is Pareto efficient. Unfortunately, competitive equilibrium prices only exist under strong assumptions such as perfectly divisible goods and convex…
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…
We analyze a quantum version of the Monge--Kantorovich optimal transport problem. The quantum transport cost related to a Hermitian cost matrix $C$ is minimized over the set of all bipartite coupling states $\rho^{AB}$ with fixed reduced…
We present a general convex relaxation approach to study a wide class of Unbalanced Optimal Transport problems for finite non-negative measures with possibly different masses. These are obtained as the lower semicontinuous and convex…
We investigate duality and existence of dual optimizers for several adapted optimal transport problems under minimal assumptions. This includes the causal and bicausal transport, the causal and bicausal barycenter problem, and a…