In the paper, the functional of selective averaging of discrete decision variables is proposed. The positive selectivity coefficient is entered into a positive decreasing kernel of functional and with growth of selectivity coefficient the mean gives optimum values (in a limit) of decision discrete variables in a problem of global optimization. Based on the estimate of the selective averaging functional, a basic global optimization algorithm is synthesized on a set of discrete variables with ordered possible values under inequality constraints. The basis is a computational scheme for optimizing continuous variables and its transformation for optimization with respect to discrete variables. On a test example the high convergence rate and a noise stability of base algorithm are shown. Simulations have shown that the estimate of the probability of making a true decision reaches unit.