Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2610.04715

GPU-Accelerated Bregman Douglas-Rachford Splitting for Discrete Optimal Transport

Yifan Xu·Shiqian Ma
View original source ↗Read source document ↗Export metadata ↓

Abstract

We present GPU-accelerated Bregman Douglas--Rachford splitting algorithm (BDRS) for discrete optimal transport problem in three input formats: an explicit cost matrix, a point cloud with a ground cost between them, and a separable cost on a regular grid. For each input format, we propose hardware-aware designs of mathematically equivalent representations for the BDRS iterations to enhance numerical stability and empirical runtime. We benchmark the three proposed implementations against eight GPU baseline solvers from the literature on the same device. We demonstrate that our implementations of BDRS achieve state-of-the-art performance on their respective input formats. To the best of our knowledge, this is the first cross-solver study of GPU DOT solvers with a unified measure of optimality.

Explore related subjects

math.OCcs.LG

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Yifan Xu, Shiqian Ma. 2026-10-03. GPU-Accelerated Bregman Douglas-Rachford Splitting for Discrete Optimal Transport. https://arxiv.org/abs/2610.04715

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Multilevel Regularized Newton Methods with Fast Convergence Rates

We introduce new multilevel methods for solving large-scale unconstrained optimization problems. Specifically, the philosophy of multilevel methods is applied to Newton-type methods that regularize the Newton sub-problem using second order information from a coarse (low dimensional) sub-problem. The new \emph{regularized multilevel methods} provably converge from any initialization point and enjoy faster convergence rates than Gradient Descent. In particular, for arbitrary functions with Lipschitz continuous Hessians, we show that their convergence rate interpolates between the rate of Gradient Descent and that of the cubic Newton method. If, additionally, the objective function is assumed to be convex, then the proposed method converges with the fast $\mathcal{O}(k^{-2})$ rate. Hence, since the updates are generated using a \emph{coarse} model in low dimensions, the theoretical results of this paper significantly speed-up the convergence of Newton-type or preconditioned gradient methods in practical applications. Preliminary numerical results suggest that the proposed multilevel algorithms are significantly faster than current state-of-the-art methods.

math.OC↗
arXiv2026

Adaptive Algorithms for Robust Phase Retrieval

This paper considers robust phase retrieval, which can be cast as a nonsmooth and nonconvex optimization problem. We propose two first-order algorithms with adaptive step sizes: the subgradient algorithm (AdaSubGrad) and the inexact proximal linear algorithm (AdaIPL). Our contribution lies in a novel design of adaptive step sizes based on quantiles of the absolute residuals. We analyze local linear convergence of both algorithms across different hyperparameter regimes under i.i.d. centered sub-Gaussian measurements, a stability condition linking the measurement distribution and the corruption level, and an additional uniform small-ball condition. Numerical experiments on synthetic datasets and image recovery also demonstrate that our methods are competitive with existing methods in the literature that utilize predetermined (possibly impractical) step sizes, such as subgradient methods and the inexact proximal linear method.

math.OC↗
arXiv2026

A Simple yet Highly Accurate Prediction-Correction Algorithm for Time-Varying Optimization

This paper proposes a simple yet highly accurate prediction-correction algorithm, SHARP, for unconstrained time-varying optimization problems. Its prediction is based on an extrapolation derived from the Lagrange interpolation of past solutions. Since this extrapolation can be computed without Hessian matrices or even gradients, the computational cost is low. To ensure the stability of the prediction, the algorithm includes an acceptance condition that rejects the prediction when the update is excessively large. The proposed method achieves a tracking error of $O(h^{p})$, where $h$ is the sampling period, assuming that the $p$-th derivative of the target trajectory is bounded and the convergence of the correction step is locally linear. We also prove that the method can track a trajectory of stationary points even if the objective function is non-convex. Numerical experiments demonstrate the high accuracy of the proposed algorithm.

math.OC↗