Concurrent Crossover for PDHG

TL;DR

This paper investigates a parallel crossover scheme for PDHG algorithms to improve solution accuracy in large-scale linear programming, aiming to combine efficiency with high precision.

Contribution

It introduces a concurrent crossover method for PDHG, enhancing solution accuracy without losing the computational advantages of first-order methods.

Findings

Concurrent crossover improves solution accuracy for PDHG.

The method maintains GPU efficiency.

Enhanced convergence speed to high-precision solutions.

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.