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

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.