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

[Barry Smith]

   Have you tried bt ? 

> On 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!
> 
> 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
> <log.txt>