A numerical method for solving an optimal control problem with fixed endpoints of trajectories and a convex functional

We propose a numerical method for solving the problem of taking a nonlinear system to the zero state while minimizing a nonnegative convex functional, whose particular cases include the problem of minimizing resource or energy consumption. The method is based on the maximum principle and approximations of solid bodies by families of simplices. The properties of coverings of solid bodies by simplices enable us to justify the convergence of the method.