cuPDLPx: A Further Enhanced GPU-Based First-Order Solver for Linear Programming

TL;DR

cuPDLPx is an advanced GPU-based linear programming solver that employs novel restart and weight update techniques, achieving significant speedups over existing methods especially in high-accuracy scenarios.

Contribution

The paper introduces cuPDLPx, a GPU-optimized first-order LP solver with new restart and primal weight update strategies, enhancing computational efficiency.

Findings

Achieves 2.5x-5x speedup on MIPLIB LP relaxations.

Attains 3x-6.8x speedup on Mittelmann's benchmarks.

Performs especially well in high-accuracy and presolve-enabled settings.

Abstract

We introduce cuPDLPx, a further enhanced GPU-based first-order solver for linear programming. Building on the recently developed restarted Halpern PDHG for LP, cuPDLPx incorporates a number of new techniques, including a new restart criterion and a PID-controlled primal weight update. These improvements are carefully tailored for GPU architectures and deliver substantial computational gains. Across benchmark datasets, cuPDLPx achieves 2.5x-5x speedups on MIPLIB LP relaxations and 3x-6.8x on Mittelmann's benchmark set, with particularly strong improvements in high-accuracy and presolve-enabled settings. The solver is publicly available at https://github.com/MIT-Lu-Lab/cuPDLPx.