It can perhaps be discerned from a tandem of StepMonitor
and EvaluationMonitor
output, say by sowing or printing how many evaluations were done in a given step. Bear in mind that a number of things could happen with the Automatic
setting, that might help to disguise the underlying method.
(1) It could decide it was in trouble (e.g. failing to meet constraints) and switch.
(2) Preprocessing might change the problem (e.g. solving linear equality constraints to remove some variables).
(3) Postprocessing, if not specifically prevented, might change the method to a local one.
I might be missing some possibilities.