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

[Binh Nguyen]

It depends on the problem you are trying to solve. If at anytime, the
hessian condition number ( http://en.wikipedia.org/wiki/Condition_number )
is large then small variation can explode into something entirely
different. At that point, numerical error (which is unavoidable when
dealing with computer floating point) can play a significant role. Good
linear solvers deal with these problems better than the others. If your
problem is "well-behaved" then I think the performance will be less
dependant on the choice of linear solver.


On Fri, Feb 17, 2012 at 9:17 AM, Joel Andersson <
joel.andersson at esat.kuleuven.be> wrote:

> 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
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>
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>
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>


-- 
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Binh Nguyen
Computer Science Department
Rensselaer Polytechnic Institute
Troy, NY, 12180
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