Related papers: Regularity of optimal transportation between space…
We study Monge's optimal transportation problem, where the cost is given by optimal control cost. We prove the existence and uniqueness of an optimal map under certain regularity conditions on the Lagrangian, absolute continuity of the…
We study the general problem of Bayesian persuasion (optimal information design) with continuous actions and continuous state space in arbitrary dimensions. First, we show that with a finite signal space, the optimal information design is…
We present the viewpoint that optimization problems encountered in machine learning can often be interpreted as minimizing a convex functional over a function space, but with a non-convex constraint set introduced by model parameterization.…
A prominent model for transportation networks is branched transport, which seeks the optimal transportation scheme to move material from a given initial to a final distribution. The cost of the scheme encodes a higher transport efficiency…
We study global optimization of non-convex functions through optimal control theory. Our main result establishes that (quasi-)optimal trajectories of a discounted control problem converge globally and practically asymptotically to the set…
Let $(X,d,m)$ be a proper, non-branching, metric measure space. We show existence and uniqueness of optimal transport maps for cost written as non-decreasing and strictly convex functions of the distance, provided $(X,d,m)$ satisfies a new…
We consider a Kantorovich potential associated to an optimal transportation problem between measures that are not necessarily absolutely continuous with respect to the Lebesgue measure, but are comparable to the Lebesgue measure when…
A remarkable connection between optimal design and Monge transport was initiated in the years 1997 in the context of the minimal elastic compliance problem and where the euclidean metric cost was naturally involved. In this paper we present…
We study stability and sample complexity properties of divergence regularized optimal transport (DOT). First, we obtain quantitative stability results for optimizers of DOT measured in Wasserstein distance, which are applicable to a wide…
Purpose: This is an attempt to better bridge the gap between the mathematical and the engineering/physical aspects of the topic. We trace the different sources of non-convexification in the context of topology optimization problems starting…
In this article, we propose a novel characterization of law-invariant and coherent risk measures, based on a generalized optimal transport problem in which the second marginal of the admissible plans is not fixed, but required to lie within…
We analyze optimal transport problems with additional entropic cost evaluated along curves in the Wasserstein space which join two probability measures $m_0,m_1$. The effect of the additional entropy functional results into an elliptic…
We consider Monge-Kantorovich optimal transport problems on $\mathbb{R}^d$, $d\ge 1$, with a convex cost function given by the cumulant generating function of a probability measure. Examples include the Wasserstein-2 transport whose cost…
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…
Complexity of the Operations Research Theory tasks can be often diminished in cases that do not require finding the exact solution. For example, forecasting two-dimensional hierarchical time series leads us to the transportation problem…
The modeling of phenomenological structure is a crucial aspect in inverse imaging problems. One emerging modeling tool in computational imaging is the optimal transport framework. Its ability to model geometric displacements across an…
In this work we consider the problem of finding the minimum-weight loop cover of an undirected graph. This combinatorial optimization problem is called 2-matching and can be seen as a relaxation of the traveling salesman problem since one…
Let $L=\DD+Z$ for a $C^1$ vector field $Z$ on a complete Riemannian manifold possibly with a boundary. By using the uniform distance, a number of transportation-cost inequalities on the path space for the (reflecting) $L$-diffusion process…
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…
Among $\R^3$-valued triples of random vectors $(X,Y,Z)$ having fixed marginal probability laws, what is the best way to jointly draw $(X,Y,Z)$ in such a way that the simplex generated by $(X,Y,Z)$ has maximal average volume? Motivated by…