Before revision:  The existence follows from an algorithm that converges from any starting point to such a point in a number of gradient and function evaluations that is polynomial in \frac{1{\epsilon}} {\varepsilon}} , the dimension d, and the bounds on f and its first three derivatives.
After revision:  The existence follows from an algorithm that converges from any starting point to such a point in a number of gradient and function evaluations that is polynomial in \frac{1{\epsilon}} \frac{1{\varepsilon}} , the dimension d, and the bounds on f and its first three derivatives.