Assume I have some non-convex function $f(x_1, x_2, ...)$ and I want to optimize it to find a global minimum. I feel like it is easy to show that this problem is in the class NP with the decision problem
Is there a set of points such that f < C?
Where C is some constant. However, I am not sure if these problems are in the class of NP-Complete, and if so, what would you say the size of the input is? Complexity of the function?