A modified Hamilton-Jacobi approach in the generalized problem of Bolza (Q762755)

In this paper sufficient conditions of zero, first and second orders are developed for the optimality of an arc x in the generalized problem of Bolza. The approach is based on modifying the Hamilton-Jacobi inequality so that it reduces to an optimization problem having x as a solution. This leads on one hand to new zero and first order criteria, on the other hand to a second order condition known in an earlier work of the author [Trans. Am. Math. Soc. 275, 561-586 (1983; Zbl 0513.49010)] by the extended Jacobi condition. This latter was first proven using canonical transformations.