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Minimizers don't work reliably on nonlinear problems
We are seeing quite a lot of strange problems in our minimizations, typically when nonlinearities are involved. So far I have not found any real bugs in our minimizers, so my suspicion is that we have to add constraints to our fields of unknowns, to prevent them wandering into regions where energy values are too high, gradients too small etc. Our current attempts to clip the nonlinearities or to manually reset the positions whenever they move out of the accepted area do not work well, so I suggest trying algorithms like SciPy's 'L-BFGS-B', 'COBYLA', etc., which have native support for constraints.
If that turns out to work well, we can try to add constraints also to our own solvers.