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?