  In this article we consider the problem of testing, for two finite sets of
points in the Euclidean space, if their convex hulls are disjoint and computing
an optimal supporting hyperplane if so. This is a fundamental problem of
classification in machine learning known as the hard-margin SVM. The problem
can be formulated as a quadratic programming problem. The SMO algorithm is the
current state of art algorithm for solving it, but it does not answer the
question of separability. An alternative to solving both problems is the
Triangle Algorithm, a geometrically inspired algorithm, initially described for
the convex hull membership problem, a fundamental problem in linear
programming. First, we describe the experimental performance of the Triangle
Algorithm for testing the intersection of two convex hulls. Next, we compare
the performance of Triangle Algorithm with SMO for finding the optimal
supporting hyperplane. Based on experimental results ranging up to 5000 points
in each set in dimensions up to 10000, the Triangle Algorithm outperforms SMO.

Computational Geometry;Data Structures and Algorithms