A parametric algorithm for the minimum norm point problem under a linear constraint and its application to portfolio optimization

We present an algorithm and its improvement for the problem of finding a minimum norm point in the intersection of the convex hull of the given finitely many points and a hyperplane defined by a linear constraint. Both of them terminate within finitely many iterations and if the given points and the normal vector of the linear constraint are integral, the number of iterations is bounded by some constant. We report some computational experiments including an actual portfolio optimization problem, which is shown to reduce to the above problem in the appendix.