Usually some form of gradient descent is combined with a global optimization routine that tries to explore the parameter space. This is nothing new, optics has been designed this way since the early 60s.
Optics equations are nonlinear (and generally nonconvex). Global optimization for nonconvex functions has not existed since the 60s. Even fast function eval (for brute force solutions) has not existed since the 60s.
Definitely not global (probably NP hard) but it’s likely optimized in some basic sense would be my guess. (Probably still using very specific parametrizations of the lenses and such.)
At some point we’ll just use metaoptics for lenses that are fully optimized using some general heuristics, but so far I am not sure they (both lenses and heuristics) are ready for prime time :)
