[petsc-dev] SNESNEWTONLS

[Matthew Knepley]

On Tue, Mar 7, 2023 at 12:03 PM Angus, Justin Ray via petsc-dev <
petsc-dev at mcs.anl.gov> wrote:

> Hi Barry,
>
>
>
> Very helpful.
>
>
>
> I’m still having some trouble with reconciling your answer to question
> number 2 based on some recent observations I have had. I’ve shared 1 slide
> concerning that observation, which I will briefly describe below.
>
>
>
> I have a code that uses petsc but also has a native JFNK solver that works
> in the standard textbook way and always uses the full newton step. I
> recently found that the SNES newton solver in petsc with default options
> was failing on step 1 of a simulation, while our native solver worked fine.
> The fix for petsc was to switch from backtracking line search to basic.
>
>
>
> Based in the information in the slide, can you make sense of this behavior?
>

Sure. It is completely possible to converge using full steps when you do
not converge using BT. All of the convergence proofs
are predicated on starting "close enough" to the solution. You can start
far away, take full steps, and by chance get into the basin of
convergence. BT, that is trying to guarantee convergence, will fail. There
are a very small number of cases for which we can
guarantee global convergence.

  Thanks,

     Matt


> -Justin
>
>
>
> *From: *Barry Smith <bsmith at petsc.dev>
> *Date: *Tuesday, March 7, 2023 at 8:52 AM
> *To: *"Angus, Justin Ray" <angus1 at llnl.gov>
> *Cc: *"petsc-dev at mcs.anl.gov" <petsc-dev at mcs.anl.gov>
> *Subject: *Re: [petsc-dev] SNESNEWTONLS
>
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> On Mar 7, 2023, at 11:36 AM, Angus, Justin Ray via petsc-dev <
> petsc-dev at mcs.anl.gov> wrote:
>
>
>
> Hello,
>
>
>
> I’ve been using the default newton line search nonlinear solver in petsc.
> I recently discovered that the default line search method is bt –
> backtracking. I have two questions.
>
>
>
>    1. How exactly does the backtracking line search use the L2 norm of
>    the function to modify the newton step? What is the formula?
>
>
>
>
> https://petsc.org/main/src/snes/linesearch/impls/bt/linesearchbt.c.html#SNESLINESEARCHBT
> <https://urldefense.us/v3/__https:/petsc.org/main/src/snes/linesearch/impls/bt/linesearchbt.c.html*SNESLINESEARCHBT__;Iw!!G2kpM7uM-TzIFchu!gRMzIDCT2gk_bmfyFDMW_2hqc18xUq_eOd-GQOXGkPsHzw_F01t55J_ab98JKVI$>
>
>
>
>
>    1.
>    2. Why is backtracking default? I would think that the basic method,
>    which is a standard Newton method, would be default.
>
>
>
>    All SNES Newton line searches use the full Newton step if it satisfies
> the Wolf conditions (there is some decrease in the function norm) and if
> the full Newton step is selected there is no nontrivial extra costs from
> using a line search (since the line search is never done) so there is no
> reason not to default to using SNESLINESEARCHBT. While using ONLY the
> full-step there may not convergence for many situations.  Hence our default.
>
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>    1.
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> -Justin
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>

-- 
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

https://www.cse.buffalo.edu/~knepley/ <http://www.cse.buffalo.edu/~knepley/>
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