An interior-point method for minimizing convex functions on the convex hull of a point set

The article describes an interior-point method for minimizing a smooth strictly convex function f: R-n -> R, f is an element of C-2(R-n), on the convex hull P of m points in R-n. The algorithm uses barycentric coordinates for representing points in P and generates points in P with positive coordinates. In particular, the algorithm can be used to compute the orthogonal projection of a point x(c) is an element of R-n to P.