Now I've read your other comment with the terminology, I think "shotgun hill-climbing" is the appropriate phrase for the sort of materials science thing I'm talking about - you start atoms in random configurations, with minimal bias, and then minimise using the forces (available analytically) on those atoms using gradient descent/whatever optimiser (usually BFGS) until you find local minima. There's no momentum involved, and the gradient is available, but you still start in random positions and minimise to local minima. That sort of method is in competition with other structure finding algorithms that use GAs, SAs or some other fudged hybrids.
My reference to "brute force" was that, as far as I understand, in the limit of lots of attempts, "shotgun" will approach "brute force" -- imagine a really nasty landscape with lots of tiny basins. I understand "stochastic ballistic" modifies things slightly.
Yes to all - thanks for the clarification. The only comment is that in large dimension cases shotgun might theoretically approach brute force, but it never does so because there are just too many places to start.
Discrete gradients are always available - you can step in random directions and re-evaluate giving an approximation. If your space is smooth(ish) (and usually it's "smooth enough") then you can use the local approximations.
Yes, sometimes it's not possible, but usually local random search gives enough to use the concept of "gradient" to help. Mostly I find that people doing the optimisation/search don't know enough about the techniques they're using to adapt them and transform their problem to get the best out of things.
Yes, but it still makes no sense to compare GA performance with a gradient-based method on the problem GP is talking about, because an explicit gradient is available.
My reference to "brute force" was that, as far as I understand, in the limit of lots of attempts, "shotgun" will approach "brute force" -- imagine a really nasty landscape with lots of tiny basins. I understand "stochastic ballistic" modifies things slightly.