This paper presents an approach to approximate the solution of the infinite horizon optimal control problem for a class of nonlinear systems. Instead of finding an approximate solution of the Hamilton-Jacobi-Bellman (HJB) equation for a given system and cost functional, a control lyapunov function (CLF) is constructed, that solves an optimal control problem for the same system but for a different and a-priori unknown cost-function. By adapting the CLF in an appropriate way, the inverse cost-function approximates the desired cost-function and therefore the found solution approximates the optimal solution. This approach does not only approximate the solution of the original optimal control problem, but it delivers the exact solution of a similar optimal control problem for the very same system.