Generalization of the Brodsky-Lepage-Mackenzie optimization within the {β}-expansion and the principle of maximal conformality

We discuss generalizations of the Brodsky-Lepage-Mackenzie optimization procedure for renormalization group invariant quantities. In this respect, we discuss in detail the features and construction of the {beta}-expansion presentation instead of the standard perturbative series with regard to the Adler D function and Bjorken polarized sum rules obtained in the order of O(alpha(4)(s)). Based on the {beta} expansion, we analyze different schemes of optimization, including the corrected principle of maximal conformality, numerically illustrating their results. We suggest our scheme for the series optimization and apply it to both the above quantities.