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I am using backtracking linesearch to globalize a (semismooth) newton solver to minimize a (strongly semismooth) strongly convex function , and I am observing something strange (which may be a bug). For some problems, I observe that the accepted step size alternates between 0 and 1 in successive iterations. On other problems, it seems to work fine.

My question is: Is it possible for Newton method to cycle (on a convex problem) when using backtracking linesearch?

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  • $\begingroup$ what system are you trying to solve/minimize? Did you check if you're near a local minima? $\endgroup$ Commented Mar 8, 2023 at 4:31
  • $\begingroup$ @helloworld922: I added some more detail, but I did check that it is not near the minimum $\endgroup$
    – jjjjjj
    Commented Mar 8, 2023 at 4:34
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    $\begingroup$ There is nothing in your post that would help anyone understand the issue. You will have to show much more detail for anyone to be able to say what is going on. In essence, all you're saying "on some problem I'm not going to tell you about, with an implementation I'm not going to show you, I'm seeing something that may or may not be suspicious". There's nothing useful anyone can tell you about the issue. $\endgroup$ Commented Mar 8, 2023 at 4:36
  • $\begingroup$ @WolfgangBangerth: thanks for the comment, I rephrased the question! $\endgroup$
    – jjjjjj
    Commented Mar 8, 2023 at 4:41
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    $\begingroup$ If you semi-smooth function in the test consists of smooth patches, then indeed such behavior is possible if the step requires a patch change. So if you are close to a patch boundary and the Newton step crosses it, and the direction is totally wrong for the next patch, then you get a small step. The next step that starts within the new patch can then proceed normally with step size $1$. $\endgroup$ Commented Mar 8, 2023 at 16:29

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