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In this paper, we provide an affirmative answer to the long-standingquestion: Are GPUs useful in solving linear programming? We present cuPDLP.jl,a GPU implementation of restarted primal-dual hybrid gradient (PDHG) forsolving linear programming (LP). We show that this prototype implementation inJulia has comparable numerical performance on standard LP benchmark sets asGurobi, a highly optimized implementation of the simplex and interior-pointmethods. Furthermore, we present the superior performance of cuPDLP.jl with itsCPU counterpart. This demonstrates the power of using GPUs in the optimizationsolvers.

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