Global Optima is not Limit Computable

Abstract

We study the limit computability of finding a global optimum of a continuous function. We give a short proof to show that the problem of checking whether a point is a global minimum is not limit computable. Thereby showing the same for the problem of finding a global minimum. In the next part, we give an algorithm that converges to the global minima when a lower bound on the size of the basin of attraction of the global minima is known. We prove the convergence of this algorithm and provide some numerical experiments.