  We present results about minimization of convex functionals defined over a
finite set of vectors in a finite dimensional Hilbert space, that extend
several known results for the Benedetto-Fickus frame potential. Our approach
depends on majorization techniques. We also consider some perturbation
problems, where a positive perturbation of the frame operator of a set of
vectors is realized as the frame operator of a set of vectors which is close to
the original one.
