Stopping test for optimization

Question

In some problems, as it is difficult to satisfy the gradient tolerance, particularly if the gradient is computed only approximately and we generally opt for the step size tolerance. Since it is important to take the scale of the problem into account in this stopping test, I am using $$ \frac{\| x(k+1) - x(k) \|}{\| x(k) \|} < \mathbf{eps}. $$ as my stopping criteria. I am interested to know if this is a good way to stop in terms of stopping criteria or can it lead to unfavourable results. Also, How can one decide the value of eps or the minimum value eps can take?