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: Rn → R, , on the convex hull P of m points in Rn . 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 xc∈ Rn to P. § Dedicated to the memory of Prof. Dr. Franti[sbreve]ek No[zbreve]i[cbreve]ka.