[petsc-users] Question regarding preconditioning in L-BFGS

[Matthew Knepley]

On Wed, Jul 1, 2015 at 7:19 AM, Michael White <mrwhite at umn.edu> wrote:

> Hello,
>
> I am not quite sure how to use the L-BFGS implementation in PETSc with a
> preconditioner that approximates the Jacobian. As far as I understand it,
> L-BFGS is like Newton's Method but doesn't require the user to input the
> Jacobian matrix. However, for my application, I do have a good
> preconditioner that approximates the Jacobian matrix. My question is where
> to input such a preconditioner. I have 3 possible guesses about the correct
> way to do it.
>
> 1. Use SNESSetJacobian to provide a function which computes the
> preconditioner. I'm unsure if this information is even used though, since
> L-BFGS builds its own approximation to the inverse Jacobian as it goes.
>
> 2. Use SNESQNSetScaleType with SNES_QN_SCALE_JACOBIAN to set my
> preconditioner as an initial approximation to the Jacobian somehow?
>

This is the intent, but we have no tests of this in PETSc, so let me know
if this works. Jed Brown and Peter Brune have a paper
where they do this and it has the options they used.


> 3. Use an SNESSetNPC with my preconditioner as a linear preconditioner?
>
> Anyone that could point me in the right direction would be greatly
> appreciated.
>

Why are you using L-BFGS if you have a good Jacobian preconditioner? You
could do Newton with that
preconditioning matrix and MF application of the Jacobian.

  Thanks,

   Matt


> Best regards,
> Michael White
>
>
>


-- 
What most experimenters take for granted before they begin their
experiments is infinitely more interesting than any results to which their
experiments lead.
-- Norbert Wiener
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