Property (a) makes the problem meaningful, since the norm is bounded below by zero. Interestingly, properties (b) and (c) imply that the norm is a convex function of h, a fact easily shown. Thus, the theory of approximations of the type illustrated above reduces to a theory of finding minima of convex functions. Such a theory has been under considerable development during the past few years, particularly in applications to linear programming and games. However, little explicit application of this theory has been made to approximation problems. Of most practical interest in the present context are norms of the form