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

Binh Nguyen nguyeb2 at cs.rpi.edu
Fri Feb 17 14:12:18 EST 2012

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
> Phone: +32-16-321819
> Mobile: +32-486-672874 (Belgium) / +34-63-4408800 (Spain) / +46-727-365878(Sweden)
> Private address: Weidestraat 5, 3000 Leuven, Belgium
> _______________________________________________
> Ipopt mailing list
> Ipopt at list.coin-or.org
> http://list.coin-or.org/mailman/listinfo/ipopt

Binh Nguyen
Computer Science Department
Rensselaer Polytechnic Institute
Troy, NY, 12180
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://list.coin-or.org/pipermail/ipopt/attachments/20120217/50a3df76/attachment.html>

More information about the Ipopt mailing list