Related papers: Duality-based Dynamical Optimal Transport of Discr…
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],…
We present a framework wherein the trajectory optimization problem (or a problem involving calculus of variations) is formulated as a search problem in a discrete space. A distinctive feature of our work is the treatment of discretization…
We study the connections between Physarum Dynamics and Dynamic Monge Kantorovich (DMK) Optimal Transport algorithms for the solution of Basis Pursuit problems. We show the equivalence between these two models and unveil their dynamic…
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…
We formulate and solve a class of finite-time transport and mixing problems in the set-oriented framework. The aim is to obtain optimal discrete-time perturbations in nonlinear dynamical systems to transport a specified initial measure on…
This paper considers decentralized dynamic optimization problems where nodes of a network try to minimize a sequence of time-varying objective functions in a real-time scheme. At each time slot, nodes have access to different summands of an…
This paper studies the distributed minimax optimization problem over networks. To enhance convergence performance, we propose a distributed optimistic gradient tracking method, termed DOGT, which solves a surrogate function that captures…
In this paper, we address the numerical solution of the Optimal Transport Problem on undirected weighted graphs, taking the shortest path distance as transport cost. The optimal solution is obtained from the long-time limit of the gradient…
In this paper, we propose a second-order continuous primal-dual dynamical system with time-dependent positive damping terms for a separable convex optimization problem with linear equality constraints. By the Lyapunov function approach, we…
A new stochastic primal--dual algorithm for solving a composite optimization problem is proposed. It is assumed that all the functions/operators that enter the optimization problem are given as statistical expectations. These expectations…
We introduce and prove convergence of a damped Newton algorithm to approximate solutions of the semi-discrete optimal transport problem with storage fees, corresponding to a problem with hard capacity constraints. This is a variant of the…
In this paper, we introduce a primal-dual algorithm for solving (martingale) optimal transportation problems, with cost functions satisfying the twist condition, close to the one that has been used recently for training generative…
First order optimization algorithms play a major role in large scale machine learning. A new class of methods, called adaptive algorithms, were recently introduced to adjust iteratively the learning rate for each coordinate. Despite great…
Optimal Transport (OT) has established itself as a robust framework for quantifying differences between distributions, with applications that span fields such as machine learning, data science, and computer vision. This paper offers a…
This paper investigates the semi-discrete optimal transport (OT) problem with entropic regularization. We characterize the solution using a governing, well-posed ordinary differential equation (ODE). This naturally yields an algorithm to…
The optimal (Monge-Kantorovich) transportation problem is discussed from several points of view. The Lagrangian formulation extends the action of the {\em Lagrangian} $L(v,x,t)$ from the set of orbits in $\R^n$ to a set of measure-valued…
We analyze controlled mass transportation plans with free end-time that minimize the transport cost induced by the generating function of a Lagrangian within a bounded domain, in addition to costs incurred as export and import tariffs at…
In this paper, we propose an inexact perturbed path-following algorithm in the framework of Lagrangian dual decomposition for solving large-scale structured convex optimization problems. Unlike the exact versions considered in literature,…
We propose a dynamic domain semi-Lagrangian method for stochastic Vlasov equations driven by transport noises, which arise in plasma physics and astrophysics. This method combines the volume-preserving property of stochastic characteristics…
We consider a continuous time stochastic optimal control problem under both equality and inequality constraints on the expectation of some functionals of the controlled process. Under a qualification condition, we show that the problem is…