Related papers: Accelerated Flow for Probability Distributions
This paper considers the decentralized convex optimization problem, which has a wide range of applications in large-scale machine learning, sensor networks, and control theory. We propose novel algorithms that achieve optimal computation…
The Poisson-Nernst-Planck system of equations used to model ionic transport is interpreted as a gradient flow for the Wasserstein distance and a free energy in the space of probability measures with finite second moment. A variational…
Convergence analysis of Nesterov's accelerated gradient method has attracted significant attention over the past decades. While extensive work has explored its theoretical properties and elucidated the intuition behind its acceleration, a…
Techniques from numerical bifurcation theory are very useful to study transitions between steady fluid flow patterns and the instabilities involved. Here, we provide computational methodology to use parameter continuation in determining…
We suggest a global perspective on dynamic network flow problems that takes advantage of the similarities to port-Hamiltonian dynamics. Dynamic minimum cost flow problems are formulated as open-loop optimal control problems for general…
The problem of minimizing a separable convex function under linearly coupled constraints arises from various application domains such as economic systems, distributed control, and network flow. The main challenge for solving this problem is…
This paper addresses the gradient flow -- the continuous-time representation of the gradient method -- with the smooth approximation of a non-differentiable objective function and presents convergence analysis framework. Similar to the…
We describe a formal procedure to obtain and specify the general form of a marginal distribution for the Lagrangian acceleration of fluid particle in developed turbulent flow using Langevin type equation and the assumption that velocity…
In this paper, we propose a novel distributed algorithm for consensus optimization over networks and a robust extension tailored to deal with asynchronous agents and packet losses. Indeed, to robustly achieve dynamic consensus on the…
Asynchronous optimization algorithms often require delay bounds to prove their convergence, though these bounds can be difficult to obtain in practice. Existing algorithms that do not require delay bounds often converge slowly. Therefore,…
In this work, we present an efficient gradient projection method for solving a class of stochastic optimal control problem with expected integral state constraint. The first order optimality condition system consisting of forward-backward…
Variational representations of divergences and distances between high-dimensional probability distributions offer significant theoretical insights and practical advantages in numerous research areas. Recently, they have gained popularity in…
Momentum methods play a significant role in optimization. Examples include Nesterov's accelerated gradient method and the conditional gradient algorithm. Several momentum methods are provably optimal under standard oracle models, and all…
(Neal and Hinton, 1998) recast maximum likelihood estimation of any given latent variable model as the minimization of a free energy functional $F$, and the EM algorithm as coordinate descent applied to $F$. Here, we explore alternative…
We propose a novel data-driven method to accelerate the convergence of Alternating Direction Method of Multipliers (ADMM) for solving distributed DC optimal power flow (DC-OPF) where lines are shared between independent network partitions.…
In this paper we bring together some of the key ideas and methods of two disparate fields of mathematical research, frame theory and optimal transport, using the methods of the second to answer questions posed in the first. In particular,…
We study distributed stochastic gradient (D-SG) method and its accelerated variant (D-ASG) for solving decentralized strongly convex stochastic optimization problems where the objective function is distributed over several computational…
The problem of minimizing convex functionals of probability distributions is solved under the assumption that the density of every distribution is bounded from above and below. A system of sufficient and necessary first-order optimality…
This paper deals with a new accelerated path integral method, which iteratively searches optimal controls with a small number of iterations. This study is based on the recent observations that a path integral method for reinforcement…
We propose a family of optimization methods that achieve linear convergence using first-order gradient information and constant step sizes on a class of convex functions much larger than the smooth and strongly convex ones. This larger…