You are given the following criterion function for a 2-class classification problem: J(w)=n=1N[[wTznxn0]]wTznxn in which augmented notation is used. Prove that J(w) is convex. Hints: (i) How can [[a0]]a be written using the max[.]function? ( [ [..]] denotes the indicator function.) (ii) You may find Discussion 4 notes on convexity helpful. Suppose you make the classifier nonlinear by using a nonlinear transformation of the feature space first: x(x) so that the criterion function is: J(w)=n=1N[[wTzn(xn)0]]wTzn(xn). Is J(w) convex? Prove your