Résumé
(ProQuest: ... denotes formulae and/or non-USASCII text omitted) A variant of variationally optimized perturbation, incorporating renormalization group properties in a straightforward way, uniquely fixes the variational mass interpolation in terms of the anomalous mass dimension. It is used at three successive orders to calculate the nonperturbative ratio F sub([pi])/[Lambda] of the pion decay constant and the basic QCD scale in the MS scheme. We demonstrate the good stability and (empirical) convergence properties of this modified perturbative series for this quantity, and provide simple and generic cures to previous problems of the method, principally the generally nonunique and nonreal optimal solutions beyond lowest order. Using the experimental F sub([pi]) input value we determine ... and ..., where the first qouted errors are our estimate of theoretical uncertainties of the method, which we consider conservative. The second uncertainties come from the present uncertainties in F sub([pi])/F and F sub([pi])/F sub(0), where F (F sub(0)) is F sub([pi]) in the exact chiral SU(2) (SU(3)) limits. Combining the [Lambda] super(n[functionof]=3) results with a standard perturbative evolution provides a new independent determination of the strong coupling constant at various relevant scales, in particular ... and ... A less conservative interpretation of our prescriptions favors central values closer to the upper limits of the first uncertainties. The theoretical accuracy is well comparable to the most precise recent single determinations of alpha sub(S), including some very recent lattice simulation determinations with fully dynamical quarks.