Gradient descent works since E(w, w0 | X) is convex w.r.t. w and w0. The convexity can be shown by showing that the Hessian matrix (i.e., second derivative) of E(.) is positive semi-definite.

(a) please compute this Hessian matrix (hint: using vector calculus directly);

(b) show that the Hessian matrix H is positive semi-definite (hint: show that for any vector x, we have x THx 0).