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

[Barry Smith]

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

In this case it could be that the computed direction is not a descent direction and hence no line search is going to help you. You need a better Jacobian.

    You can use -snes_mf_operator to use the "true" Jacobian but have the preconditioner built using the "partial Jacobian" that you provide. This makes it more likely you actually end up with a descent direction and is IMHO better than try to do Newton with an incorrect "partial Jacobian".

    Barry



> On Jan 26, 2017, at 2:20 AM, Andrew McRae <A.T.T.McRae at bath.ac.uk> wrote:
> 
> 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
>