[thxg]

I agree that their results are impressive. Just to be clear, however:

1. They compare their solver with a 1e-4 error tolerance to Gurobi with 1e-6. This may seem like a detail, but in the context of how typical LPs are formulated, this is a big difference. They have to do things this way because their solver simply isn't able to reach better accuracy (meanwhile, you can ask Gurobi for 1e-9, and it will happily comply in most cases).

2. They disable presolve, which is 100% reasonable in a scientific paper (makes things more reproducible, gives a better idea of what the solver actually does). If you look at their results to evaluate which solver you should use, though, the results will be misleading, because presolve is a huge part of what makes SOTA solvers fast.

[dsfcxv]

hmm... I am reading [1] right now. When looking at their Table 7 and Table 11 in [1], they report comparison results with Gurobi presolve enabled and 1e-8 error. Do I miss anything?

Their performance isn't quite as good as Gurobi's barrier method, but it's still within a reasonable factor, which is impressive.

[thxg]

Regarding presolve: When they test their solver "with presolve", they use Gurobi's presolve as a preprocessing step, then run their solver on the output. To be clear, this is perfectly fair, but from the perspective of "can I switch over from the solver I'm currently using", this is a big caveat.

They indeed report being 5x slower than Gurobi at 1e-8 precision on Mittelmann instances, which is great. Then again, Mittelmann himself reports them as 15x off COpt, even when allowed to do 1e-4. This is perfectly explainable (COpt is great at benchmarks; there is the presolve issue above; the Mittelmann instance set is a moving target), but I would regard the latter number as more useful from a practitioner's perspective.

This is not to diminish PDLP's usefulness. If you have a huge instance, it may be your only option!