Posted by Michael Trick on September 06, 1998 at 15:44:26:
Some questions are coming up a few times (and I at least was
quite on clear on some aspects), so here are a few clarifications:
1) If a function is convex, then any critical point (i.e. gradient
equals 0) is a maximum: you do not need the Hessian test at that
point.
2) If the functions are continuous and differentiable (and we will
assume that), and the function has a maximum (i.e. it does not go
off to infinity in the feasible boundary), then the best
of all points that satisfy K-T conditions is the optimal solution.
Again, no second derivative test is needed.