In Theorem 4.2. of the following lecture http://users.ece.utexas.edu/~cmcaram/EE381V_2012F/Lecture_4_Scribe_Notes.final.pdf
it is shown that when the objective function is smooth and not necessarily convex, by using Gradient Descent, $\nabla f(x_k)\rightarrow0$ as $k\rightarrow \infty$.
Can we conclude that $x_k$ also converges to a fixed point?