New Second-Order Optimality Conditions for Variational Problems with C[sup 2]-Hamiltonians

The generalized problem of Bolza with a C2-Hamiltonian is considered. Necessary and sufficient conditions are obtained, respectively, in terms of the accessory problem, the existence of conjoined basis, and the existence of a solution to a Riccati equation with boundary conditions. No strengthened Legendre--Clebsch condition is required. When applied to a general optimal control problem, these results include and generalize known results.

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