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Nov 23, 2012 at 9:43 comment added Thomas Rot Thus if this condition does not hold, there is a sequence such that $|\grad f(x_i)|$->0 in S. The condition forces this sequence to have a limit, and the limit must be a critical point.
Jun 14, 2012 at 5:39 comment added Thomas Rot There is no constant c>0 such that $||\nabla f||>c$ on $S$.
Jun 14, 2012 at 2:26 comment added economic Thank you for your answer. But, I cann't still understand the meaning of this sentence of $\|\nabla f\|$ is not bounded away from zero". Is $\|\nabla f\|>0$ no bounded below, and verge to 0?
May 14, 2012 at 7:34 history answered Thomas Rot CC BY-SA 3.0