  We apply the renormalization group optimized perturbation theory (RGOPT)to
evaluate the QCD (matter) pressure at the two-loop level considering three
flavors of massless quarks in a dense and cold medium. Already at leading order
($\alpha_s^0$), which builds on the simple one loop (RG resummed) term, our
technique provides a non-trivial non-perturbative approximation which is
completely renormalization group invariant. At the next-to-leading order the
comparison between the RGOPT and the pQCD predictions shows that the former
method provides results which are in better agreement with the state-of-the-art
$higher \, order$ perturbative results, which include a contribution of order
$\alpha_s^3 \ln^2 \alpha_s$. At the same time one also observes that the RGOPT
predictions are less sensitive to variations of the arbitrary $\bar{\rm MS}$
renormalization scale than those obtained with pQCD. These results indicate
that the RGOPT provides an efficient resummation scheme which may be considered
as an alternative to lattice simulations at high baryonic densities.
