← 研踪 PaperTrailarXiv:2610.04715 · v2
GPU-Accelerated Bregman Douglas-Rachford Splitting for Discrete Optimal Transport
首次提交 2026-10-04 03:08
版本更新 2026-10-28 05:42
雷达观测 2026-10-30 10:23
摘要
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.
作者备注：44 pages, 7 figures, 3 tables. Submitted to Mathematical Programming Computation
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v2 · 2026-10-28 05:42 · 最新观测版本
GPU-Accelerated Bregman Douglas-Rachford Splitting for Discrete Optimal Transport
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.
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