WiVi Y

See Appendix A.9 for the derivation of the Hessian. We have proved the statement (a). Notice that this is a contradiction because any point with WL+1 = 0 is in the set S. Hence, there exists no point at which the Hessian is negative semidefinite. Because the negative semidefiniteness is a necessary condition for a local maximum, every critical point is then either a local minimum or a saddle point. We have proved the statement (b).