[petsc-users] how to stop SNES linesearch (l^2 minimization) from choosing obviously suboptimal lambda?

[Andrew McRae]

Okay.  I discarded bt quite early since I have no reason to think the
default step size (lambda = 1) is 'good', due to the partial Jacobian.  But
I can try it again.

cp sometimes behaves well, but other times I've seen it do something crazy
like take lambda = 2.5 on the first step.  Due to the MA convexity reqs,
the linear system at the second step is then malformed and the solver dies.

I also briefly tried nleqerr in the past and found it to take a huge number
of iterations, but I can try that again.

On 25 January 2017 at 19:57, Matthew Knepley <knepley at gmail.com> wrote:

> On Wed, Jan 25, 2017 at 1:13 PM, Andrew McRae <A.T.T.McRae at bath.ac.uk>
> wrote:
>
>> I have a nonlinear problem in which the line search procedure is making
>> 'obviously wrong' choices for lambda.  My nonlinear solver options (going
>> via petsc4py) include {"snes_linesearch_type": "l2",
>> "snes_linesearch_max_it": 3}.
>>
>> After monotonically decreasing the residual by about 4 orders of
>> magnitude, I get the following...
>>
>>  15 SNES Function norm 9.211230243067e-06
>>       Line search: lambdas = [1., 0.5, 0.], fnorms = [3.13039e-05,
>> 3.14838e-05, 9.21123e-06]
>>       Line search: lambdas = [1.25615, 1.12808, 1.], fnorms =
>> [3.14183e-05, 3.13437e-05, 3.13039e-05]
>>       Line search: lambdas = [0.91881, 1.08748, 1.25615], fnorms =
>> [3.12969e-05, 3.13273e-05, 3.14183e-05]
>>       Line search terminated: lambda = 0.918811, fnorms = 3.12969e-05
>>  16 SNES Function norm 3.129688997145e-05
>>       Line search: lambdas = [1., 0.5, 0.], fnorms = [3.09357e-05,
>> 1.58135e-05, 3.12969e-05]
>>       Line search: lambdas = [0.503912, 0.751956, 1.], fnorms =
>> [1.59287e-05, 2.33645e-05, 3.09357e-05]
>>       Line search: lambdas = [0.0186202, 0.261266, 0.503912], fnorms =
>> [3.07204e-05, 9.11e-06, 1.59287e-05]
>>       Line search terminated: lambda = 0.342426, fnorms = 1.12885e-05
>>  17 SNES Function norm 1.128846081676e-05
>>       Line search: lambdas = [1., 0.5, 0.], fnorms = [3.09448e-05,
>> 5.94789e-06, 1.12885e-05]
>>       Line search: lambdas = [0.295379, 0.64769, 1.], fnorms =
>> [8.09996e-06, 4.46782e-06, 3.09448e-05]
>>       Line search: lambdas = [0.48789, 0.391635, 0.295379], fnorms =
>> [6.07286e-06, 7.07842e-06, 8.09996e-06]
>>       Line search terminated: lambda = 0.997854, fnorms = 3.09222e-05
>>  18 SNES Function norm 3.092215965860e-05
>>
>> So, in iteration 16, the lambda chosen is 0.91..., even though we see
>> that lambda close to 0 would give a smaller residual.  In iteration 18, we
>> see that some lambda around 0.65 gives a far smaller residual (approx 4e-6)
>> than the 0.997... value that gets used (which gives approx 3e-5).  The
>> nonlinear iterations then get caught in some kind of cycle until my
>> snes_max_it is reached [full log attached].
>>
>> I guess this is an artifact of (if I understand correctly) trying to
>> minimize some polynomial fitted to the evaluated values of lambda?  But
>> it's frustrating that it leads to 'obviously wrong' results!
>>
>
> There might be better line searches for this problem. For example, 'bt'
> should be more robust then 'l2', and 'cp'
> tries really hard to find a minimum. The 'nleqerr' is Deufelhard's search
> that should also be more robust. I would
> try them out to see if its better.
>
>   Matt
>
>
>> For background information, this comes from an FE discretisation of a
>> Monge-Ampère equation (and also from several timesteps into a time-varying
>> problem).  For various reasons (related to Monge-Ampère convexity
>> requirements), I use a partial Jacobian that omits a term from the
>> linearisation of the residual, and so the nonlinear convergence is not
>> expected to be quadratic.
>>
>> Andrew
>>
>
>
>
> --
> 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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