Recall that gradient descent is an optimization methodology in machine learning problems. It uses the following update rule:x_k+1=x_k-h_kf(x_k), where h_k are step size (fixed or varies across iterations). Explain (using formal mathematical rigor):-

• Why, when f is convex,h_k<2>L is the Lipschitz constant of the gradient of the function f) is a sufficient and necessary condition for the gradient descent to converge?
• Why is gradient descent problematic in non-convex problems? (Hint: look at converge to a stationary point.)