Setting the first derivative equal to zero leads to trouble, as the derivative doesn’t exist at the minimum, and there are infinitely many points which have zero slope. Nevertheless, the function has a clear minimum which gradient descent of any finite step size should find.
How about this function:
f(x) = abs(x) - cos(x)Setting the first derivative equal to zero leads to trouble, as the derivative doesn’t exist at the minimum, and there are infinitely many points which have zero slope. Nevertheless, the function has a clear minimum which gradient descent of any finite step size should find.