Dual sufficient optimality conditions for optimal control

In this paper we develop the first and second order dual sufficient optimality conditions for a nonlinear optimal control problem. Our conditions are derived from the dual Hamilton-Jacobi approach applied to the generalized problem of Bolza. We do not require neither any convexity on the data, nor that the control set U be polyhedral, nor that the control function be in the interior of U. Instead, we assume the existence of a function which satisfies a certain inequality.