  In this paper, we extend a recently established subgradient method for the
computation of Riemannian metrics that optimizes certain singular value
functions associated with dynamical systems. This extension is threefold.
First, we introduce a projected subgradient method which results in Riemannian
metrics whose parameters are confined to a compact convex set and we can thus
prove that a minimizer exists; second, we allow inexact subgradients and study
the effect of the errors on the computed metrics; and third, we analyze the
subgradient algorithm for three different choices of step sizes: constant,
exogenous and Polyak. The new methods are illustrated by application to
dimension and entropy estimation of the H\'enon map.
