Related papers: Transport multi-paths with capacity constraints
We study single commodity network flows with suitable robustness and efficiency specs. An original use of a maximum entropy problem for distributions on the paths of the graph turns this problem into a steering problem for Markov chains…
We consider the problem of finding an optimal transport plan between an absolutely continuous measure $\mu$ on $\mathcal{X} \subset \mathbb{R}^d$ and a finitely supported measure $\nu$ on $\mathbb{R}^d$ when the transport cost is the…
We consider the optimal mass transportation problem in $\RR^d$ with measurably parameterized marginals, for general cost functions and under conditions ensuring the existence of a unique optimal transport map. We prove a joint measurability…
Transit agencies have the opportunity to outsource certain services to established Mobility-on-Demand (MOD) providers. Such alliances can improve service quality, coverage, and ridership; reduce public sector costs and vehicular emissions;…
The performance of multimodal mobility systems relies on the seamless integration of conventional mass transit services and the advent of Mobility-on-Demand (MoD) services. Prior work is limited to individually improving various transport…
Connected and automated vehicles (CAVs) provide the most intriguing opportunity to improve energy efficiency, traffic flow, and safety. In earlier work, we addressed the constrained optimal coordination problem of CAVs at different traffic…
In this work, we develop a new framework for dynamic network flow problems based on optimal transport theory. We show that the dynamic multi-commodity minimum-cost network flow problem can be formulated as a multi-marginal optimal transport…
We commonly encounter the problem of identifying an optimally weight adjusted version of the empirical distribution of observed data, adhering to predefined constraints on the weights. Such constraints often manifest as restrictions on the…
Transport processes on spatial networks are representative of a broad class of real world systems which, rather than being independent, are typically interdependent. We propose a measure of utility to capture key features that arise when…
Vehicle platooning facilitates the partial automation of vehicles and can significantly reduce fuel consumption. Mobile communication infrastructure makes it possible to dynamically coordinate the formation of platoons en route. We consider…
Distribution functions of many static transport equations are found using the Maximum Entropy Principle. The equations of constraint which contain the relevant dynamical information are simply the low-lying moments of the distributions.…
This work investigates several aspects related to quantitative stability in optimal transport, as well as uniqueness of the dual transport problem. Our main contributions are as follows. Chapter 1: Observations regarding the quantitative…
In this paper, we introduce and develop the theory of semimartingale optimal transport in a path dependent setting. Instead of the classical constraints on marginal distributions, we consider a general framework of path dependent…
Recently, with the advancement of the GPS-enabled cellular technologies, the location-based services (LBS) have gained in popularity. Nowadays, an increasingly larger number of map-based applications enable users to ask a wider variety of…
We develop an $\e$-regularity theory at the boundary for a general class of Monge-Amp\`ere type equations arising in optimal transportation. As a corollary we deduce that optimal transport maps between H\"older densities supported on $C^2$…
Energy consumption is the major contributor associated with large and growing transportation cost in logistics. Optimal vehicle routing approaches can provide solutions to reduce their operating costs and address implications on energy.…
We present a systematic study of conditional triangular transport maps in function spaces from the perspective of optimal transportation and with a view towards amortized Bayesian inference. More specifically, we develop a theory of…
We use the randomization idea and proof techniques from optimal transport to study optimal reinsurance problems. We start by providing conditions for a class of problems that allow us to characterize the support of optimal treaties, and…
We study couplings $q^\bullet$ of two equivariant random measures $\lambda^\bullet$ and $\mu^\bullet$ on a Riemannian manifold $(M,d,m)$. Given a cost function we ask for minimizers of the mean transportation cost per volume. In case the…
Classic optimal transport theory is formulated through minimizing the expected transport cost between two given distributions. We propose the framework of distorted optimal transport by minimizing a distorted expected cost, which is the…