<div dir="ltr"><div class="gmail_extra"><div class="gmail_quote">On Wed, Jan 25, 2017 at 1:13 PM, Andrew McRae <span dir="ltr"><<a href="mailto:A.T.T.McRae@bath.ac.uk" target="_blank">A.T.T.McRae@bath.ac.uk</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir="ltr"><div><div>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}.<br><br></div><div>After monotonically decreasing the residual by about 4 orders of magnitude, I get the following...<br></div><div><br> 15 SNES Function norm 9.211230243067e-06 <br> Line search: lambdas = [1., 0.5, 0.], fnorms = [3.13039e-05, 3.14838e-05, 9.21123e-06]<br> Line search: lambdas = [1.25615, 1.12808, 1.], fnorms = [3.14183e-05, 3.13437e-05, 3.13039e-05]<br> Line search: lambdas = [0.91881, 1.08748, 1.25615], fnorms = [3.12969e-05, 3.13273e-05, 3.14183e-05]<br> Line search terminated: lambda = 0.918811, fnorms = 3.12969e-05<br> 16 SNES Function norm 3.129688997145e-05 <br> Line search: lambdas = [1., 0.5, 0.], fnorms = [3.09357e-05, 1.58135e-05, 3.12969e-05]<br> Line search: lambdas = [0.503912, 0.751956, 1.], fnorms = [1.59287e-05, 2.33645e-05, 3.09357e-05]<br> Line search: lambdas = [0.0186202, 0.261266, 0.503912], fnorms = [3.07204e-05, 9.11e-06, 1.59287e-05]<br> Line search terminated: lambda = 0.342426, fnorms = 1.12885e-05<br> 17 SNES Function norm 1.128846081676e-05 <br> Line search: lambdas = [1., 0.5, 0.], fnorms = [3.09448e-05, 5.94789e-06, 1.12885e-05]<br> Line search: lambdas = [0.295379, 0.64769, 1.], fnorms = [8.09996e-06, 4.46782e-06, 3.09448e-05]<br> Line search: lambdas = [0.48789, 0.391635, 0.295379], fnorms = [6.07286e-06, 7.07842e-06, 8.09996e-06]<br> Line search terminated: lambda = 0.997854, fnorms = 3.09222e-05<br> 18 SNES Function norm 3.092215965860e-05<br><br></div><div></div><div>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].<br></div><div><br></div><div>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!</div></div></div></blockquote><div><br></div><div>There might be better line searches for this problem. For example, 'bt' should be more robust then 'l2', and 'cp'</div><div>tries really hard to find a minimum. The 'nleqerr' is Deufelhard's search that should also be more robust. I would</div><div>try them out to see if its better.</div><div><br></div><div> Matt</div><div> </div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir="ltr"><div>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.<span class="HOEnZb"><font color="#888888"><br><br></font></span></div><span class="HOEnZb"><font color="#888888">Andrew<br></font></span></div>
</blockquote></div><br><br clear="all"><div><br></div>-- <br><div class="gmail_signature" data-smartmail="gmail_signature">What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead.<br>-- Norbert Wiener</div>
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