Q2.16 Assume a differentiable objective function f x is Lipschitz continuous; namely, there exists a real constant L > 0, and for any two points

Q2.16 Assume a differentiable objective function f ¹xº is Lipschitz continuous; namely, there exists a real constant L > 0, and for any two points x1 and x2, f ¹x1º ???? f ¹x2º

 L kx1 ???? x2 k always holds. Prove that the gradient descent Algorithm 2.1 always converges to a stationary point, namely, limn!1 kr f ¹x¹nººk = 0, as long as all used step sizes are small enough, satisfying n < 1L.