I want to find the global minimum of a potential energy surface with readily accessible gradients, though there is no closed form expression for this function. This function is known to be non-convex. I'm aware of stochastic methods for global optimization, like simulated annealing and genetic algorithms, but ideally I'd like a deterministic method that guarantees I find the global minimum.
There were a couple options I found, but these methods typically involve knowing the functional form of the objective function such that you can find bounds on the gradient/Hessian over an interval.
Are there deterministic algorithms that find the global optimum for black-box bounded functions with gradients?