CHChrisRackauckas·Mar 26, 2024
Definitely an interesting response I didn't see coming. This is one of the reasons to share preprints!
IPOPT is a nonlinear optimization tool, not a nonlinear solver. Generally from what I've seen it's not a good idea to solve nonlinear systems with a nonlinear optimizer, but you can phrase it as a "constraint satisfaction problem", i.e. a nonlinear optimization with a trivial `maximize 0` loss function but with equality constraints to be satisfied `f(u) = 0` and allow it to do that. IIRC the sparse symmetric linear solver is only used in the optimization process as it's that part where it can guarantee a sparse symmetric linear system, the constraints themselves `f` would have to be symmetric to reuse that in the Newton method which isn't true for any of the benchmarks. As such, I don't think you'd get most of IPOPT's advantages even sho
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wing up in a constraint satisfaction problem at all. Don't get me wrong, IPOPT is an amazing software for nonlinear optimization, but when not doing optimization it would lose a lot of what makes it amazing.
However, perfectly agreed that I cannot lay this to rest right now because I don't have a benchmark to point to. The best thing to do here would be to add it to the benchmarks and fully describe why in the paper. We'll definitely follow up with this in a revision.
In the meantime, if you have more requests for the benchmarks, please feel free to open issues at https://github.com/SciML/SciMLBenchmarks.jl so we can track them. All of our benchmarks run on this open platform and anyone can add things via a PR. In particular, the 23 benchmarks diagram in the paper for example is simply just the result of this script https://github.com/SciML/SciMLBenchmarks.jl/blob/master/benc... which runs automatically on any PR (for new folks it requires we click yes for security reasons though). So please feel free to send any benchmark requests. We do plan to do a lot more comprehensive nonlinear optimization benchmarks in the near future. For this case with IPOPT though, we're happy to add that in ourselves hopefully in the next few weeks.