The paper discusses various approaches to solving nonlinear optimal control problems. Of all such approaches, we chose the two most characteristic. The first one uses sufficient conditions of optimality in the form of Hamilton–Jacobi–Bellman equations and the corresponding numerical method. The second is based on the reduction of optimal control problem to interval linear programming problem and finding a solution using the Gabasov’s adaptive method. The main goal is to compare the capabilities of these methods within a specific problem of optimal control. As an application, we consider the problem of constructing optimal control in a nonlinear model of macroeconomic growth with nonlinear dynamical constraints. Comparative analysis of these two approaches and corresponding numerical simulation are presented.