相关论文: On semi-discrete sub-partitions of vector-valued m…

We revisit the duality theorem for multimarginal optimal transportation problems. In particular, we focus on the Coulomb cost. We use a discrete approximation to prove equality of the extremal values and some careful estimates of the…

We introduce the proximal optimal transport divergence, a novel discrepancy measure that interpolates between information divergences and optimal transport distances via an infimal convolution formulation. This divergence provides a…

We consider an optimal transport problem with backward martingale constraint. The objective function is given by the scalar product of a pseudo-Euclidean space $S$. We show that the supremums over maps and plans coincide, provided that the…

We propose new variational principles for traffic assignment problems. So to find equillibrium we have to solve large-scale convex optimization problem of special type. We propose some kind of "algebra" on different models and corresponding…

We introduce a semi-supervised learning estimator which tends to the first kernel principal component as the number of labelled points vanishes. Our approach is based on the notion of optimal target vector, which is defined as follows.…

We investigate electron transport through clean open quantum dots (quantum billiards). We present a semiclassical theory that allows to accurately reproduce quantum transport calculations. Quantitative agreement is reached for individual…

We study different notions of slope of a vector bundle over a smooth projective curve with respect to ampleness and affineness in order to apply this to tight closure problems. This method gives new degree estimates from above and from…

We investigate the approximation of Monge--Kantorovich problems on general compact metric spaces, showing that optimal values, plans and maps can be effectively approximated via a fully discrete method. First we approximate optimal values…

Efficient algorithms for solving optimal transport problems are important for measuring and optimizing distances between functions. In the $L^2$ semi-discrete context, this problem consists of finding a map from a continuous density…

We present an Initial Value Representation for the semiclassical coherent state propagator based on complex trajectories. We map the complex phase space into a real phase space with twice as many dimensions and use a simple procedure to…

Continuity of the value of the martingale optimal transport problem on the real line w.r.t. its marginals was recently established in Backhoff-Veraguas and Pammer [2] and Wiesel [21]. We present a new perspective of this result using the…

Set- and vector-valued optimization problems can be re-formulated as complete lattice-valued problems. This has several advantages, one of which is the existence of a clear-cut solution concept which includes the attainment as the infimum…

We extend the Caffarelli-Cordoba estimates to the vector case in two ways, one of which has no scalar counterpart, and we give a few applications for minimal solutions.

Discrete barycenters are the optimal solutions to mass transport problems for a set of discrete measures. Such transport problems arise in many applications of operations research and statistics. The best known algorithms for exact…

We show that a class of Poincar\'e-Wirtinger inequalities on bounded convex sets can be obtained by means of the dynamical formulation of Optimal Transport. This is a consequence of a more general result valid for convex sets, possibly…

L multiple descriptions of a vector Gaussian source for individual and central receivers are investigated. The sum rate of the descriptions with covariance distortion measure constraints, in a positive semidefinite ordering, is exactly…

We propose a new embedding method for a single vector and for a pair of vectors. This embedding method enables: a) efficient classification and regression of functions of single vectors; b) efficient approximation of distance functions; and…

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…

We present a 2-step optimal transport approach that performs a mapping from a source distribution to a target distribution. Here, the target has the particularity to present new classes not present in the source domain. The first step of…

This work considers semi-supervised segmentation as a dense prediction problem based on prototype vector correlation and proposes a simple way to represent each segmentation class with multiple prototypes. To avoid degenerate solutions, two…