Related papers: Variational models of robust optimal transport
Several problems in machine learning are naturally expressed as the design and analysis of time-evolving probability distributions. This includes sampling via diffusion methods, optimizing the weights of neural networks, and analyzing the…
In this paper, we study the optimal transport problem induced by separable cost functions. In this framework, transportation can be expressed as the composition of two lower-dimensional movements. Through this reformulation, we prove that…
In this paper, we consider the problem of optimizing the trajectory of an Unmanned Aerial Vehicle (UAV) Base Station (BS). We consider a map characterized by a traffic intensity of users to be served. The UAV BS must travel from a given…
Optimizing passengers routes is crucial to design efficient transportation networks. Recent results show that optimal transport provides an efficient alternative to standard optimization methods. However, it is not yet clear if this…
This paper presents a novel robust trajectory optimization method for constrained nonlinear dynamical systems subject to unknown bounded disturbances. In particular, we seek optimal control policies that remain robustly feasible with…
In this paper, a green transportation location problem is considered with uncertain demand parameter. Increasing robustness influences the number of trucks for sending goods and products, and consequently, makes the air pollution enhance.…
This paper focuses on designing edge-weighted networks, whose robustness is characterized by maximizing algebraic connectivity, or the second smallest eigenvalue of the Laplacian matrix. This problem is motivated by cooperative vehicle…
Optimal deployment and movement of multiple unmanned aerial vehicles (UAVs) is studied. The considered scenario consists of several ground terminals (GTs) communicating with the UAVs using variable transmission power and fixed data rate.…
A new pairwise cost function is proposed for the optimal transport barycenter problem, adopting the form of the minimal action between two points, with a Lagrangian that takes into account an underlying probability distribution. Under this…
First we present two classical models of Branched Transport: the Lagrangian model introduced by Bernot, Caselles, Morel, Maddalena, Solimini, and the Eulerian model introduced by Xia. An emphasis is put on the Lagrangian model, for which we…
The Eulerian variational formulation of the gyrokinetic system with electrostatic turbulence is presented in general spatial coordinates by extending our previous work [H. Sugama, {\it et al}., Phys.\ Plasmas {\bf 25}, 102506 (2018)]. The…
A hybrid Eulerian-Lagrangian method is proposed to simulate passive scalar transport on arbitrary shape interface. In this method, interface deformation is tracked by an Eulerian method while the transport of the passive scalar on the…
In this paper, we propose the optimal production transport model, which is an extension of the classical optimal transport model. We observe in economics, the production of the factories can always be adjusted within a certain range, while…
In this paper we study a variant of the branched transportation problem, that we call multi-material transport problem. This is a transportation problem, where distinct commodities are transported simultaneously along a network. The cost of…
We consider a class of convex optimization problems modelling temporal mass transport and mass change between two given mass distributions (the so-called dynamic formulation of unbalanced transport), where we focus on those models for which…
We consider the line planning problem in public transportation, under a robustness perspective. We present a mechanism for robust line planning in the case of multiple line pools, when the line operators have a different utility function…
This paper is devoted to variational problems on the set of probability measures which involve optimal transport between unequal dimensional spaces. In particular, we study the minimization of a functional consisting of the sum of a term…
Global infrastructure robustness and local transport efficiency are critical requirements for transportation networks. However, since passengers often travel greedily to maximize their own benefit and trigger traffic jams, overall…
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…
Optimal transport (OT) is known to be sensitive against outliers because of its marginal constraints. Outlier robust OT variants have been proposed based on the definition that outliers are samples which are expensive to move. In this…