Related papers: Computational Semi-Discrete Optimal Transport with…
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…
In minimum-cost inverse optimization problems, we are given a feasible solution to an underlying optimization problem together with a linear cost function, and the goal is to modify the costs by a small deviation vector so that the input…
This chapter describes techniques for the numerical resolution of optimal transport problems. We will consider several discretizations of these problems, and we will put a strong focus on the mathematical analysis of the algorithms to solve…
We derive nearly tight and non-asymptotic convergence bounds for solutions of entropic semi-discrete optimal transport. These bounds quantify the stability of the dual solutions of the regularized problem (sometimes called Sinkhorn…
We study the convergence rate of Sinkhorn's algorithm for solving entropy-regularized optimal transport problems when at least one of the probability measures, $\mu$, admits a density over $\mathbb{R}^d$. For a semi-concave cost function…
In this paper, we present a distributed algorithm for solving convex, constraint-coupled, optimization problems over peer-to-peer networks. We consider a network of processors that aim to cooperatively minimize the sum of local cost…
We study the Neural Optimal Transport (NOT) algorithm which uses the general optimal transport formulation and learns stochastic transport plans. We show that NOT with the weak quadratic cost might learn fake plans which are not optimal. To…
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…
We present a discretization of the dynamic optimal transport problem for which we can obtain the convergence rate for the value of the transport cost to its continuous value when the temporal and spatial stepsize vanish. This convergence…
In this paper, we study a dynamic pickup and delivery problem with docking constraints. There is a homogeneous fleet of vehicles to serve pickup-and-delivery requests at given locations. The vehicles can be loaded up to their capacity,…
We consider the problem of optimally allocating a given total storage budget in a distributed storage system. A source has a data object which it can code and store over a set of storage nodes; it is allowed to store any amount of coded…
We propose a self-organization scheme for cost-effective and load-balanced routing in multi-hop networks. To avoid overloading nodes that provide favourable routing conditions, we assign each node with a cost function that penalizes high…
We propose a discrete time formulation of the semi-martingale optimal transport problem based on multi-marginal entropic transport. This approach offers a new way to formulate and solve numerically the calibration problem proposed by [17],…
Caching can be leveraged to significantly improve network performance and mitigate congestion. However, characterizing the optimal tradeoff between routing cost and cache deployment cost remains an open problem. In this paper, for a network…
Nonlinear programming problems are useful in designing and assigning work schedule and also in transporting goods and services from known sources to specified destinations. The objective function could be linear or nonlinear depending on…
We study stability of optimizers and convergence of Sinkhorn's algorithm for the entropic optimal transport problem. In the special case of the quadratic cost, our stability bounds imply that if one of the two entropic potentials is…
This paper proposes a locally differentially private federated learning algorithm for strongly convex but possibly nonsmooth problems that protects the gradients of each worker against an honest but curious server. The proposed algorithm…
This paper studies distributed continuous-time optimization for time-varying quadratic cost functions with uncertain parameters. We first propose a centralized adaptive optimization algorithm using partial information of the cost function.…
Carrier Sense Multiple Access (CSMA) based distributed algorithms can attain the largest capacity region as the centralized Max-Weight policy does. Despite their capability of achieving throughput-optimality, these algorithms can either…
This paper studies a combined space partitioning and network flow optimization problem, with applications to large-scale power, transportation, or communication systems. In dense wireless networks, one may want to simultaneously optimize…