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What are the advantages (if any) of using IPOPT with HSL vs MUMPS? HSL has a reputation of being faster, but does it walk the walk? In particular, does HSL scale better for large-scale problems?

We have been using IPOPT with MUMPS in our engine and every time we solve anything remotely large (e.g. >50000 variables) MUMPS lights up like a Christmas tree in the profiler. Therefore, I was wondering whether HSL (maybe MA57) would make a noticable difference over MUMPS. The most recent comparison I could find is not very relevant as it's ten years old and doesn't measure IPOPT's performance, which is what I'm interested in.

I've never really been one to trust benchmarks, so I'm really interested in hands-on experience people might have using IPOPT with HSL. I should also note that our solver uses MPI, so we have to use MUMPS in serial mode.

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This question happened to appear only a couple days after Byron Tasseff, Carleton Coffrin, Andreas Wächter, and Carl Laird (the last two are the original authors of IPOPT together with Larry Biegler) uploaded the following paper in arXiV.

The paper compares the different Linear Solvers (and potential parallelization schemes) performance within IPOPT. They perform a really thorough computational comparison using both CUTEr instances and other more challenging cases. I will just include the last table in the manuscript here:

Taken from [1]

Since you also wanted some hands-on experience I can share mine with IPOPT. Every time I need to use it and do have access to the HSL licenses (academic), it does not take long for me to switch to HSL licensed solvers (I have good experiences with MA57, MA 86 (non-deterministic) and MA 97). I have yet to try PARDISO and SPRAL (I will try it after reading the paper on arXiv I mentioned).

Finally, some more benchmarks appear in the original paper of MA57, where they have a full comparison against MA27 within optimization solvers (tables 13 and 14). Although old (2002), the codes have not changed and I would expect the same trend today.

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