Related papers: Some Aspects on Solving Transportation Problem
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…
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 study the Lagrangian formulation of a class of the Monge-Kantorovich optimal transportation problem. It can be considered a stochastic optimal transportation problem for absolutely continuous stochastic processes. A cost function and…
This paper deals with the existence of optimal transport maps for some optimal transport problems with a convex but non strictly convex cost. We give a decomposition strategy to address this issue. As part of our strategy, we have to treat…
The branched transport problem, a popular recent variant of optimal transport, is a non-convex and non-smooth variational problem on Radon measures. The so-called urban planning problem, on the contrary, is a shape optimization problem that…
The classical problem of optimal transportation can be formulated as a linear optimization problem on a convex domain: among all joint measures with fixed marginals find the optimal one, where optimality is measured against a cost function.…
Optimal transportation theory is an area of mathematics with real-world applications in fields ranging from economics to optimal control to machine learning. We propose a new algorithm for solving discrete transport (network flow) problems,…
We shall present a measure theoretical approach for which together with the Kantorovich duality provide an efficient tool to study the optimal transport problem. Specifically, we study the support of optimal plans where the cost function…
A probabilistic method for solving the Monge-Kantorovich mass transport problem on $R^d$ is introduced. A system of empirical measures of independent particles is built in such a way that it obeys a doubly indexed large deviation principle…
In this work, we construct a novel numerical method for solving the multi-marginal optimal transport problems with Coulomb cost. This type of optimal transport problems arises in quantum physics and plays an important role in understanding…
In the classical Monge-Kantorovich problem, the transportation cost only depends on the amount of mass sent from sources to destinations and not on the paths followed by this mass. Thus, it does not allow for congestion effects. Using the…
Consider the problem of optimally matching two measures on the circle, or equivalently two periodic measures on the real line, and suppose the cost of matching two points satisfies the Monge condition. We introduce a notion of locally…
Optimal transportation problem seeks for a coupling $\pi$ of two probability measures $\mu$ and $\nu$ which minimize the total cost $\int c d\pi$, which is linear in $\pi$. In this paper, we introduce a variation of optimal transportation…
Many problems in geometric optics or convex geometry can be recast as optimal transport problems: this includes the far-field reflector problem, Alexandrov's curvature prescription problem, etc. A popular way to solve these problems…
It is well-known that the optimal transport problem on the real line for the classical distance cost may not have a unique solution. In this paper we recover uniqueness by considering the transport problems where the costs are a power…
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 Kantorovich type optimal transportation problems with nonlinear cost functions, including dependence on conditional measures of transport plans. A range of nonlinear Kantorovich problems for cost functions of a special form is…
In this paper, we present a numerical method, based on iterative Bregman projections, to solve the optimal transport problem with Coulomb cost. This is related to the strong interaction limit of Density Functional Theory. The first idea is…
In this note, we introduce a class of indicators that enable to compute efficiently optimal transport plans associated to arbitrary distributions of $N$ demands and $N$ supplies in $\mathbf{R}$ in the case where the cost function is…
Optimal maps, solutions to the optimal transportation problems, are completely determined by the corresponding c-convex potential functions. In this paper, we give simple sufficient conditions for a smooth function to be c-convex when the…