Abstract
In this paper we develop first and second order sufficient conditions for optimal control and the calculus of variations problems. Our conditions are derived from the Hamilton-Jacobi approach [15, Thm. 2], which was obtained for the generalized problem of Bolza. We do not require any convexity on the data [7] and [11], or that the control setU is polyhedral [14], or that the control function is in the interior ofU [8]. Instead, we assume a certain inequality which is satisfied in each of the above mentioned cases.
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