Convergence of an upwind finite-difference scheme for Hamilton-Jacobi-bellman equation in optimal control

This technical note considers convergence of an upwind finite-difference numerical scheme for the Hamilton-Jacobi-Bellman equation arising in optimal control. This effective scheme has been well-adapted and successfully applied to many examples. Nevertheless, its convergence has remained open until now. In this note, we show that the solution from this finite-difference scheme converges to the value function of the associated optimal control problem.