Analytic QCD running coupling constant and minimality principle for nonperturbative contributions in the ultraviolet region

The problem of whether the hypothesis of the freezing of the QCD running coupling constant in the infrared region is consistent with the equations of motion is considered. It is shown that freezing is not realized if there are no kinematical singularities in the transverse part of the three-gluon vertex function. The expression for the running coupling constant is modified with allowance for the minimality principle formulated for non-perturbative contributions in the ultraviolet region. It is shown that, for the case of the running coupling constant, the requirements of asymptotic freedom, analyticity, and confinement can be made consistent with the magnitude of the gluon condensate.