Linear programming (LP) problems have long been crucial in computer science and operations research, impacting various sectors of the economy. Traditional LP methods struggle with large instances due to memory overflow and hardware-related challenges. First-order methods (FOMs) like PDLP offer a scalable solution, utilizing matrix-vector multiplication and reducing memory usage. PDLP, which won the prestigious Beale — Orchard-Hays Prize, improves upon the primal-dual hybrid gradient to enhance convergence and efficiency. PDLP has diverse applications, including data center traffic engineering, container shipping optimization, and solving massive traveling salesman problems. Continual advancements, such as GPU implementations and commercial integrations, demonstrate the broad impact of PDLP in computational optimization.
https://research.google/blog/scaling-up-linear-programming-with-pdlp/