Solution
= Solution
Use the uniform lower step bound from part (iv):
$$
0\leq\|g(x_k)\|_2^2\leq\frac{\alpha_k\|g(x_k)\|_2^2}{\alpha_{\min}}\longrightarrow0.
$$
Thus $\boxed{g(x_k)\to0}$. This is convergence to stationarity in the usual global convergence theorem for the <steepest descent method>. It does not itself prove that the iterates converge, or that any stationary limit is a global minimizer of a nonconvex objective.