Concurrent Crossover for PDHG
Edward Rothberg
TL;DR
This work investigates accelerating PDHG-based linear programming on GPUs by introducing a concurrent crossover scheme that launches multiple crossover attempts from diverse PDHG iterates. By exploiting parallelism, the approach aims to produce a high-quality basic feasible solution without waiting for full PDHG convergence, achieving notable runtime reductions (25–50% on average) in practice. The authors validate the method on CPU and GPU platforms using Mittelmann and PDHG-friendly model sets, showing significant speedups on CPUs and meaningful improvements on GPUs, while also highlighting scenarios where conventional LP solvers remain faster. Overall, the paper demonstrates that concurrent crossover can mitigate PDHG’s slower convergence and deliver practical gains for large-scale LP solving on modern heterogeneous architectures.
Abstract
First-order methods based on the PDHG algorithm have recently emerged as a viable option for efficiently solving large-scale linear programming problems. One highly desirable property of these methods is that they can make effective use of GPUs. One undesirable property is that, as first-order methods, their convergence can be extremely slow. This property forces one to decide how much accuracy is truly necessary when solving an LP problem. This paper looks at whether a parallel, concurrent crossover scheme can help to obtain highly accurate solutions without sacrificing the benefits of these new approaches.