The problem of finding an extremum for a non-stationary objective function is considered, when its values, depending on the components of the control vector, are specified only in a discrete set of time points. To find a solution, a discrete gradient method of unconditional optimization is proposed. The conditions of its application are formulated. An estimate of the lower limit of the solution error due to the magnitude of the step in time and the rate of change of the objective function and estimates of its second derivatives of the components of the control vector are obtained. The application of the method is demonstrated on a numerical model of an extreme regulator designed to control a non-stationary object with a nonlinear objective function.