Related papers: Stability for the mailing problem
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…
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…
A general theory is provided delivering convergence of maximal cyclically monotone mappings containing the supports of coupling measures of sequences of pairs of possibly random probability measures on Euclidean space. The theory is based…
We analyze the pattern forming ability and pattern stability for a one-dimensional non-linear transport-diffusion equation on the circle. We show that the trivial steady state is stable when diffusion is sufficiently strong. In the limit…
This paper shows that the semi-dual formulation of the optimal transport problem has a degenerate saddle-point structure, and that its numerical solution is equivalent to solving a constrained optimization problem. We derive necessary and…
We study tracking-type optimal control problems that involve a non-affine, weak-to-weak continuous control-to-state mapping, a desired state $y_d$, and a desired control $u_d$. It is proved that such problems are always nonuniquely solvable…
It is shown that optimal network plans can be obtained, naturally, as a limit of easier problems of point allocations. These problems are obtained by minimizing the mass transportation on the set of atomic measures of prescribed number of…
Consider the set of probability measures with given marginal distributions on the product of two complete, separable metric spaces, seen as a correspondence when the marginal distributions vary. In problems of optimal transport, continuity…
The optimal transport problem with quadratic regularization is useful when sparse couplings are desired. The density of the optimal coupling is described by two functions called potentials; equivalently, potentials can be defined as a…
We provide a new proof of the known partial regularity result for the optimal transportation map (Brenier map) between two sets. Contrary to the existing regularity theory for the Monge-Amp{\`e}re equation, which is based on the maximum…
We present and study the Static-Routing-Resiliency problem, motivated by routing on the Internet: Given a graph $G$, a unique destination vertex $d$, and an integer constant $c>0$, does there exist a static and destination-based routing…
The Ring Loading Problem is an optimal routing problem arising in the planning of optical communication networks which use bidirectional SONET rings. In mathematical terms, it is an unsplittable multicommodity flow problem on undirected…
We prove existence and uniqueness of solutions, continuous dependence from the initial datum and stability with respect to the boundary condition in a class of initial--boundary value problems for systems of balance laws. The particular…
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…
In its most general form, the optimal transport problem is an infinite-dimensional optimization problem, yet certain notable instances admit closed-form solutions. We identify the common source of this tractability as \textit{symmetry} and…
We study the problem of maximizing a spectral risk measure of a given output function which depends on several underlying variables, whose individual distributions are known but whose joint distribution is not. We establish and exploit an…
We analyzed the stability of the uniform flow solution in the optimal velocity model for traffic and granular flow under the open boundary condition. It was demonstrated that, even within the linearly unstable region, there is a parameter…
This article generalizes the study of branched/ramified optimal transportation to those with capacity constraints. Each admissible transport network studied here is represented by a transport multi-path between measures, with a capacity…
We study the design of one-to-one matching mechanisms that are strategy-proof for both sides and as stable as possible. Motivated by the impossibility result of Roth (1982), we formulate the mechanism design problem as a linear program that…
This paper studies a variant of ramified/branched optimal transportation problems. Given the distributions of production capacities and market sizes, a firm looks for an allocation of productions over factories, a distribution of sales…