cuPDLP.jl: A GPU Implementation of Restarted Primal-Dual Hybrid Gradient for Linear Programming in Julia

In this paper, we provide an affirmative answer to the long-standing question: Are GPUs useful in solving linear programming? We present cuPDLP.jl, a GPU implementation of restarted primal-dual hybrid gradient (PDHG) for solving linear programming (LP). We show that this prototype implementation in Julia has comparable numerical performance on standard LP benchmark sets to Gurobi, a highly optimized implementation of the simplex and interior-point methods. This demonstrates the power of using GPUs in linear programming, which, for the first time, showcases that GPUs and first-order methods can lead to performance comparable to state-of-the-art commercial optimization LP solvers on standard benchmark sets.