On a convex function useful in determination of linear discriminant functions

The problem of determining a linear discriminant function to minimize probability of error in distinguishing between two measurement classes may, as is well known, often be approximated by a problem of minimizing some convex function. Many particular convex functions have been proposed for this purpose. While the relations between the real problem and the approximation are of critical importance, such relations are frequently unclear or even unsatisfactory. Here we examine a particular choice and show that it has a collection of desirable attributes, relating to the real problem, which are not known to be possessed by any other choice.