It is well known that a convex function is minimised over a convex set, if and only if there is a subgradient which is inwards normal to the set at that point. i.e the negative subgradient (direction of steepest decrease) points directly out of the set.
Is there a corresponding rule for maximising a convex function? i.e is beig maximised at a point equivalent to having a subgradient that is normal outwardsto the set at that point. i.e the direction of steepest increase points directly out of the set.