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 as Gurobi, a highly optimized implementation of the simplex and interior-point methods. Furthermore, we present the superior performance of cuPDLP.jl with its CPU counterpart. This demonstrates the power of using GPUs in the optimization solvers.