  We provide new complexity information for the convergence of the Hybrid
Steepest Descent Method for solving the Variational Inequality Problem for a
strict contraction on Hilbert space over a closed convex set C given either as
the fixed point set of a single nonexpansive mapping or the intersection of the
fixed point sets of a finite family of nonexpansive mappings. More precisely,
we give metastability rates in the sense of Tao for those cases. The results in
this paper were extracted from a proof due to Yamada using proof-mining
techniques, and provide a thorough quantitative analysis of the Hybrid Steepest
Descent Method.
