#ill-conditioning

Question 1: Single choice

Gradient descent with a fixed learning rate is very slow on $f(\mathbf{x}) = x_1^2 + 100x_2^2$ . What is the cause?

Keeping $x_2$ stable needs $\eta < 0.01$ , and then $x_1$ shrinks by at most 2% per step1
The gradient along $x_1$ is zero away from the axis, so $x_1$ never moves2
The minimum is not unique, so the iterates drift along a flat valley of equally good points3
The function is not convex, so the iterates bounce between local minima4