Sort of. It depends on the learning algorithm used. Typically some form of local optimization is used that gets it to a good local optima. This is usually good

Sort of. It depends on the learning algorithm used. Typically some form of local optimization is used that gets it to a good local optima. This is usually good enough and fast. However you can use methods of global optimizations or whatever optimization algorithm you want to use. NNs themselves are sort of agnostic to the algorithm you use to set their weights. It's sort of like saying "computers are Turing complete, but can we ever prove that human programmers are smart enough to program any function."