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Newton or Dogleg?
Posted 02.10.2012, 01:59 GMT-4 Studies & Solvers Version 4.3 1 Reply
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Hallo,
does anyone of you have experience with the new double dogleg solver (which is an option for
nonlinear solving and can replace the Newton-method)?
I have a nonlinear stationary problem (electromagnetic) where the damped Newton solver takes
~100 steps and uses a small damping factor for most of the steps. The dogleg solver
on the other side has fewer steps and they are mainly undamped Newton-steps. So
I wonder why the Newton solver is so bad.
But this does not generalise to all my cases, sometimes the Newton works just fine.
What are your experiences here? Are there configuration settings to push the Newton-solver to
higher damping factors? Is there a good literature reference explaining the double-dogleg
algorithm?
Thanks in advance.
Regards
Jens
does anyone of you have experience with the new double dogleg solver (which is an option for
nonlinear solving and can replace the Newton-method)?
I have a nonlinear stationary problem (electromagnetic) where the damped Newton solver takes
~100 steps and uses a small damping factor for most of the steps. The dogleg solver
on the other side has fewer steps and they are mainly undamped Newton-steps. So
I wonder why the Newton solver is so bad.
But this does not generalise to all my cases, sometimes the Newton works just fine.
What are your experiences here? Are there configuration settings to push the Newton-solver to
higher damping factors? Is there a good literature reference explaining the double-dogleg
algorithm?
Thanks in advance.
Regards
Jens
1 Reply Last Post 02.10.2012, 09:07 GMT-4
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Posted:
1 decade ago
Hi Jens,
The new Double Dogleg solver according to the COMSOL documentation is a “sophisticated combination of the Steepest descent and Newton-Raphson methods”. The basic idea is that away from the solution (especially of nonlinear constrained problems) the Newton method can easily fail, while the gradient methods guarantee progress (even if slow) towards a minimum (could be a local one). At the vicinity of the solution however the Newton method has the best convergence rate. The new Double Dogleg solver intelligently combines the two methods to generate a good overall solver. It belongs to a broader type of solvers called Trust Region solvers. The credit of developing this algorithm it seems goes to this reference: www.springerlink.com/content/m33j465v5r565215/.
Comparing the Newton and Double Dogleg solvers for the problems I work on, I found that in some cases the new solver works much better and in some cases it didn’t and I switched back to the Newton method. I could have gone to COMSOL Support to try to fine tune the Double Dogleg settings for these problems, but it’s not worth it for me when another solver is working!
Nagi Elabbasi
Veryst Engineering
The new Double Dogleg solver according to the COMSOL documentation is a “sophisticated combination of the Steepest descent and Newton-Raphson methods”. The basic idea is that away from the solution (especially of nonlinear constrained problems) the Newton method can easily fail, while the gradient methods guarantee progress (even if slow) towards a minimum (could be a local one). At the vicinity of the solution however the Newton method has the best convergence rate. The new Double Dogleg solver intelligently combines the two methods to generate a good overall solver. It belongs to a broader type of solvers called Trust Region solvers. The credit of developing this algorithm it seems goes to this reference: www.springerlink.com/content/m33j465v5r565215/.
Comparing the Newton and Double Dogleg solvers for the problems I work on, I found that in some cases the new solver works much better and in some cases it didn’t and I switched back to the Newton method. I could have gone to COMSOL Support to try to fine tune the Double Dogleg settings for these problems, but it’s not worth it for me when another solver is working!
Nagi Elabbasi
Veryst Engineering