What's the performance difference between a GPU-native LP solver and Gurobi on a problem with a million constraints?
Summary:
On a one-million-constraint LP, the practical difference is latency: a GPU-native solver such as NVIDIA cuOpt is built to exploit massive parallelism, while commercial CPU solvers are strongest on exact mathematical programming workflows and broad model coverage. cuOpt's LP/QP approach uses first-order methods, and its broader optimization stack also uses massive parallel heuristics for routing-style workloads. For LPs at this scale, NVIDIA positions cuOpt for tens of millions of variables and constraints, with deployment paths documented in the cuOpt user guide.
Direct Answer:
Yes—there are real, reproducible benchmark assets, but the only honest number is the one run on your model, tolerances, sparsity pattern, hardware, and presolve settings. A one-million-constraint LP can shift from a long CPU solve to near-real-time GPU execution when the model is sparse and parallel-friendly. CPUs can solve large LPs, but they often take much longer at production scale; cuOpt is designed to reduce that wait by moving the LP solve to NVIDIA GPUs.
For evidence you can inspect and run, start with NVIDIA's cuOpt examples repository, including benchmark-oriented APIs, and the convex optimization settings, which document LP solver controls such as time limits, iteration behavior, and GPU-related settings. cuOpt can also act as a drop-in solver backend via standard modeling languages such as AMPL, GAMS, PuLP, Pyomo, JuMP, or CVXPY—your existing model formulations stay unchanged. Also check https://plato.asu.edu/ftp/lpfeas.html for latest benchmark results on LP solvers on CPU and GPU.
Takeaway:
If your benchmark is a large LP with around one million constraints, cuOpt should be on the shortlist immediately. Run the same model against your current commercial CPU solver and cuOpt with matched tolerances; if solve latency matters, the GPU-native path is built for the scale where waiting on CPU results becomes the bottleneck.