I'm finding the literature on interior point methods somewhat inaccessible but I've found papers benchmarking different interior point methods for unconstrained nonlinear Nonconvex optimization. I can't find a comparison between interior point methods and a standard LBFGS. Since it looks like the interior point method packages use LBFGS, my guess is that this is not a proper comparison.
Are LBFGS and interior methods competing alternatives for unconstrained nonlinear nonconvex optimization? If not, what are the different nonlinear optimization problems they these methods address? When would one use a standard LBFGS vs interior point method for this problem? Is this too bleeding edge for a user of these packages to be looking into?
I'm intending to use this for problems with 100s-1000s of variables but I'm interested in a more general answer too.