Related papers: Duality-based Dynamical Optimal Transport of Discr…
This article studies unbalanced optimal transport (UOT) and its dynamical extension, unbalanced density control (UDC), for a class of constrained discrete-time linear systems. UOT compares measures with unequal total mass by balancing…
This work is concerned with the efficient optimization method for solving a large class of optimal mass transport problems. An inexact primal-dual algorithm is presented from the time discretization of a proper dynamical system, and by…
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…
We study differentially private (DP) algorithms for stochastic convex optimization: the problem of minimizing the population loss given i.i.d. samples from a distribution over convex loss functions. A recent work of Bassily et al. (2019)…
The emergence of bandwidth-intensive latency-critical traffic in 5G Networks, such as Virtual Reality, has motivated interest in wireless resource allocation problems for flows with hard-deadlines. Attempting to solve this problem brings…
In this paper, a projected primal-dual gradient flow of augmented Lagrangian is presented to solve convex optimization problems that are not necessarily strictly convex. The optimization variables are restricted by a convex set with…
We propose a distributed first-order augmented Lagrangian (DFAL) algorithm to minimize the sum of composite convex functions, where each term in the sum is a private cost function belonging to a node, and only nodes connected by an edge can…
We consider a decentralized optimization problem for networks affected by communication delays. Examples of such networks include collaborative machine learning, sensor networks, and multi-agent systems. To mimic communication delays, we…
We design and compute first-order implicit-in-time variational schemes with high-order spatial discretization for initial value gradient flows in generalized optimal transport metric spaces. We first review some examples of gradient flows…
Differential Dynamic Programming (DDP) has become a well established method for unconstrained trajectory optimization. Despite its several applications in robotics and controls however, a widely successful constrained version of the…
Numerical global optimization methods are often very time consuming and could not be applied for high-dimensional nonconvex/nonsmooth optimization problems. Due to the nonconvexity/nonsmoothness, directly solving the primal problems…
In this paper we introduce a new class of finite element discretizations of the quadratic optimal transport problem based on its dynamical formulation. These generalize to the finite element setting the finite difference scheme proposed by…
This article devises a new numerical method for first-order transport problems by using the primal-dual weak Galerkin (PD-WG) finite element method recently developed in scientific computing. The PD-WG method is based on a variational…
Optimizing problems in a distributed manner is critical for systems involving multiple agents with private data. Despite substantial interest, a unified method for analyzing the convergence rates of distributed optimization algorithms is…
The theory of Optimal Transport (OT) and Martingale Optimal Transport (MOT) were inspired by problems in economics and finance and have flourished over the past decades, making significant advances in theory and practice. MOT considers the…
We propose new continuous-time formulations for first-order stochastic optimization algorithms such as mini-batch gradient descent and variance-reduced methods. We exploit these continuous-time models, together with simple Lyapunov analysis…
In this work, a flexible higher-order space-time adaptive finite element approximation of convection-dominated transport with coupled fluid flow is developed and studied. Convection-dominated transport is a challenging subproblem in…
In this paper we present distributed and adaptive algorithms for motion coordination of a group of m autonomous vehicles. The vehicles operate in a convex environment with bounded velocity and must service demands whose time of arrival,…
We present a parallelized primal-dual algorithm for solving constrained convex optimization problems. The algorithm is "block-based," in that vectors of primal and dual variables are partitioned into blocks, each of which is updated only by…
Numerical methods for the optimal transport problem is an active area of research. Recent work of Kitagawa and Abedin shows that the solution of a time-dependent equation converges exponentially fast as time goes to infinity to the solution…