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

[Matthew Knepley]

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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