[Ipopt] Why is the choice of the linear solver so important for convergence?

[Joel Andersson]

Hello!

I have often seen a large difference in performance of Ipopt, not just in
the time per iteration, but in the number of iterations between the
different linear solvers.

Do you have a simple explaination for this? I mean, since they are all
direct sparse linear solvers, one would expect the linear system to be
solved with high accuracy, and then it shouldn't really matter for Ipopt,
which solver is used.

With some kind of iterative refinement of the solution, would you then
expect all of the solvers to perform equally (again, not in terms of time,
but in the steps taken)?

Best,
Joel

-- 
Joel Andersson, PhD Student
Electrical Engineering Department (ESAT-SCD), Room 05.11,
K.U.Leuven, Kasteelpark Arenberg 10 - bus 2446, 3001 Heverlee, Belgium
Phone: +32-16-321819
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Private address: Weidestraat 5, 3000 Leuven, Belgium
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