The problem of object management in conditions of uncertainty, when there is no formalized description, and measurements are made at certain intervals, is considered. It is assumed that the dependence of the objective function on the control parameter is quite smooth and does not have sharp jumps. The construction of control mechanisms in such a situation is associated with the problem of an extreme regulator that automatically searches for and maintains the extreme value of the regulated value. The problem boils down to the problem of finding the extremum for a nonstationary objective function, when its values, depending on the components of the control vector, are set only on a discrete set of moments. To find a solution, a discrete method of unconditional optimization of the gradient type is proposed. The conditions of its application are considered. The application of the method is demonstrated on the numerical model of an extreme regulator designed to manage a non-stationary object with a nonlinear objective function of tax revenues from the tax rate.